Conducting Flat Drops in a Confining Potential
We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a parameter measuring the relative strength of the Coulomb int...
Saved in:
| Published in: | Archive for rational mechanics and analysis Vol. 243; no. 3; pp. 1773 - 1810 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2022
Springer Nature B.V |
| Subjects: | |
| ISSN: | 0003-9527, 1432-0673 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a parameter measuring the relative strength of the Coulomb interaction. As a consequence, when the potential is confining and the Coulomb repulsion strength is below a critical value, we show existence and regularity estimates for volume-constrained minimizers. We also derive the Euler–Lagrange equation satisfied by regular critical points, expressing the first variation of the Coulombic energy in terms of the normal
1
2
-derivative of the capacitary potential. |
|---|---|
| AbstractList | We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a parameter measuring the relative strength of the Coulomb interaction. As a consequence, when the potential is confining and the Coulomb repulsion strength is below a critical value, we show existence and regularity estimates for volume-constrained minimizers. We also derive the Euler–Lagrange equation satisfied by regular critical points, expressing the first variation of the Coulombic energy in terms of the normal
1
2
-derivative of the capacitary potential. We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a parameter measuring the relative strength of the Coulomb interaction. As a consequence, when the potential is confining and the Coulomb repulsion strength is below a critical value, we show existence and regularity estimates for volume-constrained minimizers. We also derive the Euler–Lagrange equation satisfied by regular critical points, expressing the first variation of the Coulombic energy in terms of the normal 12-derivative of the capacitary potential. |
| Author | Muratov, Cyrill B. Ruffini, Berardo Novaga, Matteo |
| Author_xml | – sequence: 1 givenname: Cyrill B. orcidid: 0000-0002-3337-6165 surname: Muratov fullname: Muratov, Cyrill B. email: muratov@njit.edu organization: Department of Mathematical Sciences, New Jersey Institute of Technology – sequence: 2 givenname: Matteo surname: Novaga fullname: Novaga, Matteo organization: Department of Mathematics, University of Pisa – sequence: 3 givenname: Berardo surname: Ruffini fullname: Ruffini, Berardo organization: Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, Dipartimento di Matematica, Alma Mater Studiorum – Università di Bologna |
| BookMark | eNp9kMFKAzEQhoNUsK2-gKcFz6mTZDfZPUq1KhT0oOeQzSYlZU3WJD349m5dQfDQ0zDM_80M3wLNfPAGoWsCKwIgbhMAhQoDJRiIYDWGMzQnJaMYuGAzNAcAhpuKigu0SGl_bCnjc7RaB98ddHZ-V2x6lYv7GIZUOF-oYhxZ54-T15CNz071l-jcqj6Zq9-6RO-bh7f1E96-PD6v77ZYM9Jk3GigNXBeVw0zDDph2tpYJUrDuaqs0UILsJ22qu2oaRktK1u1dSlAM6p5w5boZto7xPB5MCnLfThEP56UlNO6BFbxckzVU0rHkFI0VmqXVXbB56hcLwnIox052ZGjHfljR8KI0n_oEN2Hil-nITZBaQz7nYl_X52gvgH8xHem |
| CitedBy_id | crossref_primary_10_3233_ASY_231853 crossref_primary_10_1007_s10231_025_01608_6 crossref_primary_10_1080_03605302_2025_2511919 |
| Cites_doi | 10.1007/s00205-014-0827-9 10.1098/rspa.1964.0151 10.1103/PhysRevLett.106.144501 10.1080/14786448208628425 10.1063/1.857551 10.1007/978-3-642-65183-0 10.1016/j.bulsci.2011.12.004 10.1103/PhysRevE.89.033011 10.4007/annals.2008.168.941 10.1007/s00205-010-0383-x 10.1007/PL00011302 10.1007/s00332-015-9259-4 10.1017/CBO9781139108133 10.1002/(SICI)1096-9888(199707)32:7<677::AID-JMS536>3.0.CO;2-G 10.1051/cocv/2012041 10.5565/PUBLMAT_60116_01 10.1007/s00205-003-0298-x 10.1007/s10404-015-1603-3 10.1007/s10231-016-0632-1 10.1090/S0002-9939-2014-12381-1 10.1146/annurev.fluid.39.050905.110245 10.4171/RMI/902 10.1146/annurev.fluid.39.050905.110159 10.2140/apde.2018.11.1113 10.1007/BF02937431 10.1137/20M1346584 10.1002/cpa.21739 10.1155/2019/8283496 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature 2022 The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature 2022. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature 2022 – notice: The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature 2022. |
| DBID | AAYXX CITATION 3V. 7SC 7TB 7XB 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ HCIFZ JQ2 K7- KR7 L6V L7M L~C L~D M0N M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.1007/s00205-021-01738-0 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection (subscription) ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology collection ProQuest One Community College ProQuest Central Engineering Research Database ProQuest Central Student SciTech Premium ProQuest Computer Science Collection Computer Science Database Civil Engineering Abstracts ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Engineering Database (subscription) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Databases ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering collection ProQuest Central Basic |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts ProQuest Computing Engineering Database ProQuest Central Basic ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) |
| DatabaseTitleList | Computer Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics Physics |
| EISSN | 1432-0673 |
| EndPage | 1810 |
| ExternalDocumentID | 10_1007_s00205_021_01738_0 |
| GrantInformation_xml | – fundername: Division of Mathematical Sciences grantid: 1614948; 1908709 funderid: http://dx.doi.org/10.13039/100000121 – fundername: Università di Pisa grantid: PRA 2017-18 funderid: http://dx.doi.org/10.13039/501100007514 – fundername: Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni funderid: http://dx.doi.org/10.13039/100012740 – fundername: Agence Nationale de la Recherche grantid: ANR-18-CE40-0013 SHAPO funderid: http://dx.doi.org/10.13039/501100001665 |
| GroupedDBID | --Z -54 -5F -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 23M 28- 29~ 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6J9 6NX 6TJ 78A 8FE 8FG 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDBF ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFO ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACNCT ACOKC ACOMO ACPIV ACREN ACUHS ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFDYV AFEXP AFGCZ AFKRA AFLOW AFQWF AFWTZ AFYQB AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAGR AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMTXH AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. B0M BA0 BBWZM BDATZ BENPR BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DWQXO EAD EAP EBLON EBS EIOEI EJD EMK EPL ESBYG ESX FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GPTSA GQ6 GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K6V K7- KDC KOV KOW L6V LAS LLZTM M0N M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9T PF0 PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDH SDM SGB SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPH SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UPT UTJUX UZXMN VC2 VFIZW VH1 VXZ W23 W48 WH7 WK8 YLTOR Z45 Z7Y Z7Z Z83 Z8S Z8T Z8W Z92 ZMTXR ZY4 ~8M ~EX AADXB AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 3V. 7SC 7TB 7XB 8AL 8FD 8FK FR3 JQ2 KR7 L7M L~C L~D PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c319t-9c0280668593e30d7eb8efa74e66a5fec7c70fdcfabd2eb3245f5b8470c32c693 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 6 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000749935000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0003-9527 |
| IngestDate | Wed Nov 05 14:42:58 EST 2025 Tue Nov 18 20:15:34 EST 2025 Sat Nov 29 06:03:47 EST 2025 Fri Feb 21 02:47:42 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c319t-9c0280668593e30d7eb8efa74e66a5fec7c70fdcfabd2eb3245f5b8470c32c693 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-3337-6165 |
| PQID | 2628403564 |
| PQPubID | 326363 |
| PageCount | 38 |
| ParticipantIDs | proquest_journals_2628403564 crossref_citationtrail_10_1007_s00205_021_01738_0 crossref_primary_10_1007_s00205_021_01738_0 springer_journals_10_1007_s00205_021_01738_0 |
| PublicationCentury | 2000 |
| PublicationDate | 20220300 2022-03-00 20220301 |
| PublicationDateYYYYMMDD | 2022-03-01 |
| PublicationDate_xml | – month: 3 year: 2022 text: 20220300 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationTitle | Archive for rational mechanics and analysis |
| PublicationTitleAbbrev | Arch Rational Mech Anal |
| PublicationYear | 2022 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | Schmidt (CR36) 2015; 143 Goldman, Novaga, Ruffini (CR20) 2015; 217 Basaran, Scriven (CR4) 1989; 1 Muratov, Novaga, Ruffini (CR30) 2018; 71 Fernández de la Mora (CR13) 2007; 39 CR19 Ros-Oton (CR34) 2016; 60 Garzon, Gray, Sethian (CR17) 2014; 89 Lieb, Loss (CR25) 2001 Esposito, Fusco (CR12) 2011; 18 Ros-Oton, Serra (CR35) 2017; 196 Taylor (CR37) 1964; 280 Fontelos, Friedman (CR15) 2004; 172 Choksi, Muratov, Topaloglu (CR7) 2017; 64 Di Nezza, Palatucci, Valdinoci (CR11) 2012; 136 Castro-Hernandez, García-Sánchez, Tan, Gañán-Calvo, Baret, Ramos (CR6) 2015; 19 Figalli, Maggi (CR14) 2011; 201 Novaga, Ruffini (CR31) 2015; 22 Barrero, Loscertales (CR3) 2007; 39 De Silva, Savin (CR10) 2016; 32 Burton, Taborek (CR5) 2011; 106 Dalibard, Gérard-Varet (CR8) 2013; 19 Landkof (CR24) 1972 Mennucci (CR28) 2019; 2019 Gaskell (CR18) 1997; 32 CR9 Maggi (CR27) 2012 Muratov, Novaga (CR29) 2016; 472 Lu, Moroz, Muratov (CR26) 2015; 25 Ambrosio, Tilli (CR2) 2004 Rayleigh (CR33) 1882; 14 Goldman, Novaga, Ruffini (CR21) 2018; 11 Iglesias, Mercier (CR23) 2021; 53 Hofmann, Mitrea, Taylor (CR22) 2007; 17 Fusco, Maggi, Pratelli (CR16) 2008; 2 Pólya, Szegö (CR32) 1951 Ambrosio, Caselles, Masnou, Morel (CR1) 2001; 3 A Figalli (1738_CR14) 2011; 201 E Di Nezza (1738_CR11) 2012; 136 SJ Gaskell (1738_CR18) 1997; 32 JA Iglesias (1738_CR23) 2021; 53 R Choksi (1738_CR7) 2017; 64 G Pólya (1738_CR32) 1951 1738_CR19 F Maggi (1738_CR27) 2012 D De Silva (1738_CR10) 2016; 32 J Fernández de la Mora (1738_CR13) 2007; 39 T Schmidt (1738_CR36) 2015; 143 C Muratov (1738_CR30) 2018; 71 J Lu (1738_CR26) 2015; 25 JC Burton (1738_CR5) 2011; 106 M Goldman (1738_CR21) 2018; 11 M Garzon (1738_CR17) 2014; 89 L Esposito (1738_CR12) 2011; 18 M Novaga (1738_CR31) 2015; 22 X Ros-Oton (1738_CR34) 2016; 60 MA Fontelos (1738_CR15) 2004; 172 L Ambrosio (1738_CR2) 2004 N Fusco (1738_CR16) 2008; 2 S Hofmann (1738_CR22) 2007; 17 X Ros-Oton (1738_CR35) 2017; 196 A Mennucci (1738_CR28) 2019; 2019 1738_CR9 A Barrero (1738_CR3) 2007; 39 EH Lieb (1738_CR25) 2001 C Muratov (1738_CR29) 2016; 472 E Castro-Hernandez (1738_CR6) 2015; 19 NS Landkof (1738_CR24) 1972 Lord Rayleigh (1738_CR33) 1882; 14 L Ambrosio (1738_CR1) 2001; 3 M Goldman (1738_CR20) 2015; 217 A-L Dalibard (1738_CR8) 2013; 19 G Taylor (1738_CR37) 1964; 280 OA Basaran (1738_CR4) 1989; 1 |
| References_xml | – volume: 217 start-page: 1 year: 2015 end-page: 36 ident: CR20 article-title: Existence and stability for a non-local isoperimetric model of charged liquid drops publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-014-0827-9 – volume: 280 start-page: 383 year: 1964 end-page: 397 ident: CR37 article-title: Disintegration of water drops in an electric field publication-title: Proc. R. Soc. Lond. A doi: 10.1098/rspa.1964.0151 – volume: 106 start-page: 144501 year: 2011 ident: CR5 article-title: Simulations of Coulombic fission of charged inviscid drops publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.106.144501 – volume: 14 start-page: 184 year: 1882 end-page: 186 ident: CR33 article-title: On the equilibrium of liquid conducting masses charged with electricity publication-title: Philos. Mag. doi: 10.1080/14786448208628425 – volume: 1 start-page: 795 year: 1989 end-page: 798 ident: CR4 article-title: Axisymmetric shapes and stability of isolated charged drops publication-title: Phys. Fluids A doi: 10.1063/1.857551 – year: 1972 ident: CR24 publication-title: Foundations of Modern Potential Theory doi: 10.1007/978-3-642-65183-0 – volume: 22 start-page: 1125 year: 2015 end-page: 1134 ident: CR31 article-title: Brunn–Minkowski inequality for the -Riesz capacity and level set convexity for the -Laplacian publication-title: J. Convex Anal. – year: 1951 ident: CR32 publication-title: Isoperimetric Inequalities in Mathematical Physics – volume: 136 start-page: 521 issue: 5 year: 2012 end-page: 573 ident: CR11 article-title: Hitchhiker’s guide to the fractional Sobolev spaces publication-title: Bull. Sci. Math. doi: 10.1016/j.bulsci.2011.12.004 – volume: 64 start-page: 1275 year: 2017 end-page: 1283 ident: CR7 article-title: An old problem resurfaces nonlocally: Gamow’s liquid drops inspire today’s research and applications publication-title: Not. Am. Math. Soc. – volume: 89 start-page: 033011 year: 2014 ident: CR17 article-title: Numerical simulations of electrostatically driven jets from nonviscous droplets publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.033011 – volume: 2 start-page: 941 issue: 168 year: 2008 end-page: 980 ident: CR16 article-title: The sharp quantitative isoperimetric inequality publication-title: Ann. Math. doi: 10.4007/annals.2008.168.941 – volume: 201 start-page: 143 issue: 1 year: 2011 end-page: 207 ident: CR14 article-title: On the shape of liquid drops and crystals in the small mass regime publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-010-0383-x – volume: 3 start-page: 39 issue: 1 year: 2001 end-page: 92 ident: CR1 article-title: Connected components of sets of finite perimeter and applications to image processing publication-title: J. Eur. Math. Soc. doi: 10.1007/PL00011302 – volume: 25 start-page: 1391 issue: 6 year: 2015 end-page: 1430 ident: CR26 article-title: Orbital-free density functional theory of out-of-plane charge screening in graphene publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-015-9259-4 – year: 2012 ident: CR27 publication-title: Sets of Finite Perimeter and Geometric Variational Problems. An Introduction to Geometric Measure Theory. Cambridge Studies in Advanced Mathematics, 135 doi: 10.1017/CBO9781139108133 – volume: 32 start-page: 677 year: 1997 end-page: 688 ident: CR18 article-title: Electrospray: principles and practice publication-title: J. Mass Spectrom. doi: 10.1002/(SICI)1096-9888(199707)32:7<677::AID-JMS536>3.0.CO;2-G – volume: 18 start-page: 417 issue: 2 year: 2011 end-page: 426 ident: CR12 article-title: A remark on a free interface problem with volume constraint publication-title: Convex Anal. – volume: 19 start-page: 976 year: 2013 end-page: 1013 ident: CR8 article-title: On shape optimization problems involving the fractional Laplacian publication-title: ESAIM Control Optim. Calc. Var. doi: 10.1051/cocv/2012041 – year: 2004 ident: CR2 publication-title: Topics on Analysis in Metric Spaces. Oxford Lecture Series in Mathematics and its Applications, 25 – year: 2001 ident: CR25 publication-title: Analysis. Graduate Studies in Mathematics, 14 – volume: 60 start-page: 3 issue: 1 year: 2016 end-page: 26 ident: CR34 article-title: Nonlocal elliptic equations in bounded domains: a survey publication-title: Publ. Mat. doi: 10.5565/PUBLMAT_60116_01 – volume: 172 start-page: 267 year: 2004 end-page: 294 ident: CR15 article-title: Symmetry-breaking bifurcations of charged drops publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-003-0298-x – ident: CR19 – volume: 19 start-page: 787 year: 2015 end-page: 794 ident: CR6 article-title: Breakup length of AC electrified jets in a microfluidic flow focusing junction publication-title: Microfluid. Nanofluid. doi: 10.1007/s10404-015-1603-3 – volume: 196 start-page: 1637 issue: 5 year: 2017 end-page: 1668 ident: CR35 article-title: Boundary regularity estimates for nonlocal elliptic equations in and domains publication-title: Ann. Mat. Pura Appl. doi: 10.1007/s10231-016-0632-1 – volume: 143 start-page: 2069 issue: 5 year: 2015 end-page: 2084 ident: CR36 article-title: Strict interior approximation of sets of finite perimeter and functions of bounded variation publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-2014-12381-1 – volume: 39 start-page: 89 year: 2007 end-page: 106 ident: CR3 article-title: Micro- and nanoparticles via capillary flows publication-title: Annu. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.39.050905.110245 – volume: 32 start-page: 891 issue: 3 year: 2016 end-page: 912 ident: CR10 article-title: Boundary Harnack estimates in slit domains and applications to thin free boundary problems publication-title: Rev. Mat. Iberoam. doi: 10.4171/RMI/902 – volume: 39 start-page: 217 year: 2007 end-page: 243 ident: CR13 article-title: The fluid dynamics of Taylor cones publication-title: J. Ann. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.39.050905.110159 – volume: 11 start-page: 1113 issue: 5 year: 2018 end-page: 1142 ident: CR21 article-title: On minimizers of an isoperimetric problem with long-range interactions and convexity constraint publication-title: Anal. PDE doi: 10.2140/apde.2018.11.1113 – ident: CR9 – volume: 17 start-page: 593 issue: 4 year: 2007 end-page: 647 ident: CR22 article-title: Geometric and transformational properties of Lipschitz domains, Semmes–Kenig–Toro domains, and other classes of finite perimeter domains publication-title: J. Geom. Anal. doi: 10.1007/BF02937431 – volume: 53 start-page: 1509 issue: 2 year: 2021 end-page: 1545 ident: CR23 article-title: Convergence of level sets in total variation denoising through variational curvatures in unbounded domains publication-title: SIAM J. Math. Anal. doi: 10.1137/20M1346584 – volume: 71 start-page: 1049 issue: 6 year: 2018 end-page: 1073 ident: CR30 article-title: On equilibrium shapes of charged flat drops publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.21739 – volume: 472 start-page: 20150808 year: 2016 ident: CR29 article-title: On well-posedness of variational models of charged drops publication-title: Proc. R. Soc. Lond. A – volume: 2019 start-page: 8283496 year: 2019 ident: CR28 article-title: On perimeters and volumes of fattened sets publication-title: Int. J. Math. Math. Sci. doi: 10.1155/2019/8283496 – volume: 1 start-page: 795 year: 1989 ident: 1738_CR4 publication-title: Phys. Fluids A doi: 10.1063/1.857551 – volume: 39 start-page: 89 year: 2007 ident: 1738_CR3 publication-title: Annu. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.39.050905.110245 – ident: 1738_CR19 – volume-title: Isoperimetric Inequalities in Mathematical Physics year: 1951 ident: 1738_CR32 – volume: 2 start-page: 941 issue: 168 year: 2008 ident: 1738_CR16 publication-title: Ann. Math. doi: 10.4007/annals.2008.168.941 – volume: 280 start-page: 383 year: 1964 ident: 1738_CR37 publication-title: Proc. R. Soc. Lond. A doi: 10.1098/rspa.1964.0151 – volume: 172 start-page: 267 year: 2004 ident: 1738_CR15 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-003-0298-x – volume: 196 start-page: 1637 issue: 5 year: 2017 ident: 1738_CR35 publication-title: Ann. Mat. Pura Appl. doi: 10.1007/s10231-016-0632-1 – volume: 22 start-page: 1125 year: 2015 ident: 1738_CR31 publication-title: J. Convex Anal. – volume: 14 start-page: 184 year: 1882 ident: 1738_CR33 publication-title: Philos. Mag. doi: 10.1080/14786448208628425 – volume: 143 start-page: 2069 issue: 5 year: 2015 ident: 1738_CR36 publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-2014-12381-1 – volume: 32 start-page: 677 year: 1997 ident: 1738_CR18 publication-title: J. Mass Spectrom. doi: 10.1002/(SICI)1096-9888(199707)32:7<677::AID-JMS536>3.0.CO;2-G – volume: 89 start-page: 033011 year: 2014 ident: 1738_CR17 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.033011 – volume: 472 start-page: 20150808 year: 2016 ident: 1738_CR29 publication-title: Proc. R. Soc. Lond. A – volume: 201 start-page: 143 issue: 1 year: 2011 ident: 1738_CR14 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-010-0383-x – volume-title: Topics on Analysis in Metric Spaces. Oxford Lecture Series in Mathematics and its Applications, 25 year: 2004 ident: 1738_CR2 – volume-title: Foundations of Modern Potential Theory year: 1972 ident: 1738_CR24 doi: 10.1007/978-3-642-65183-0 – volume: 3 start-page: 39 issue: 1 year: 2001 ident: 1738_CR1 publication-title: J. Eur. Math. Soc. doi: 10.1007/PL00011302 – volume: 11 start-page: 1113 issue: 5 year: 2018 ident: 1738_CR21 publication-title: Anal. PDE doi: 10.2140/apde.2018.11.1113 – ident: 1738_CR9 – volume: 136 start-page: 521 issue: 5 year: 2012 ident: 1738_CR11 publication-title: Bull. Sci. Math. doi: 10.1016/j.bulsci.2011.12.004 – volume: 19 start-page: 976 year: 2013 ident: 1738_CR8 publication-title: ESAIM Control Optim. Calc. Var. doi: 10.1051/cocv/2012041 – volume-title: Analysis. Graduate Studies in Mathematics, 14 year: 2001 ident: 1738_CR25 – volume: 71 start-page: 1049 issue: 6 year: 2018 ident: 1738_CR30 publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.21739 – volume: 60 start-page: 3 issue: 1 year: 2016 ident: 1738_CR34 publication-title: Publ. Mat. doi: 10.5565/PUBLMAT_60116_01 – volume: 2019 start-page: 8283496 year: 2019 ident: 1738_CR28 publication-title: Int. J. Math. Math. Sci. doi: 10.1155/2019/8283496 – volume: 18 start-page: 417 issue: 2 year: 2011 ident: 1738_CR12 publication-title: Convex Anal. – volume: 32 start-page: 891 issue: 3 year: 2016 ident: 1738_CR10 publication-title: Rev. Mat. Iberoam. doi: 10.4171/RMI/902 – volume: 64 start-page: 1275 year: 2017 ident: 1738_CR7 publication-title: Not. Am. Math. Soc. – volume: 25 start-page: 1391 issue: 6 year: 2015 ident: 1738_CR26 publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-015-9259-4 – volume: 217 start-page: 1 year: 2015 ident: 1738_CR20 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-014-0827-9 – volume: 19 start-page: 787 year: 2015 ident: 1738_CR6 publication-title: Microfluid. Nanofluid. doi: 10.1007/s10404-015-1603-3 – volume: 53 start-page: 1509 issue: 2 year: 2021 ident: 1738_CR23 publication-title: SIAM J. Math. Anal. doi: 10.1137/20M1346584 – volume: 39 start-page: 217 year: 2007 ident: 1738_CR13 publication-title: J. Ann. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.39.050905.110159 – volume: 17 start-page: 593 issue: 4 year: 2007 ident: 1738_CR22 publication-title: J. Geom. Anal. doi: 10.1007/BF02937431 – volume-title: Sets of Finite Perimeter and Geometric Variational Problems. An Introduction to Geometric Measure Theory. Cambridge Studies in Advanced Mathematics, 135 year: 2012 ident: 1738_CR27 doi: 10.1017/CBO9781139108133 – volume: 106 start-page: 144501 year: 2011 ident: 1738_CR5 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.106.144501 |
| SSID | ssj0003236 |
| Score | 2.3818915 |
| Snippet | We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1773 |
| SubjectTerms | Classical Mechanics Complex Systems Confining Critical point Digital Object Identifier Energy Euler-Lagrange equation Fluid- and Aerodynamics Mathematical and Computational Physics Physics Physics and Astronomy Theoretical Two dimensional models Variational geometry |
| SummonAdditionalLinks | – databaseName: ProQuest Central dbid: BENPR link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3PS8MwFH7o5kEPTqfidEoO3rSaNk2znETnhhfHEIXdSpOmMBjtXKt_v0mWdSi4i7dC2xDy8n4l730fwFWIM6HDbO5xmaZe6AvhJT3he0wGBjAtVYxLSzbBRqPeZMLH7sCtdGWVK5toDXVaSHNGfhdE2pBiQqPwfv7hGdYoc7vqKDS2oWmQyvQ-bz4ORuPX2haTwJIEmieP04C5thnbPGciJdOdbNJpptUe_3RN63jz1xWp9TzD1n_nfAD7LuZED8tNcghbKm9Dy8WfyGl32Ya9lxrDtTyC236RGzBYPSc0nCUVeloU8xJNc5Qg0ydomSXQuKhMvVEyO4b34eCt_-w5dgVParWrtHDsrWpkAM8UwSlToqeyhIUqihKaKckkw1kqs0SkgU65g5BmVGhnhiUJZMTJCTTyIlengIgvsKJKZ04RCakUnFKS4JARwXkoVNoBf7WwsXTQ44YBYxbXoMlWGLEWRmyFEeMOXNf_zJfAGxu_7q4kEDslLOP18nfgZiXD9eu_RzvbPNo57AamCcJWonWhUS0-1QXsyK9qWi4u3Rb8Bp3r3p4 priority: 102 providerName: ProQuest |
| Title | Conducting Flat Drops in a Confining Potential |
| URI | https://link.springer.com/article/10.1007/s00205-021-01738-0 https://www.proquest.com/docview/2628403564 |
| Volume | 243 |
| WOSCitedRecordID | wos000749935000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: SpringerLink Contemporary customDbUrl: eissn: 1432-0673 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0003236 issn: 0003-9527 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1RS8MwED50U9AHp1NxOksefNNK2zTN8qjTIYhjOJXhS2nSFAajHWv195tkbYeigr6UlqZJucvl7ri77wDOfCfhysxmNhNxbPsu53bU465NhacB02JJmTDNJuhw2JtM2KgsCsurbPcqJGlO6rrYTVs2uppYu79Uialy1JtEo81oH338Up-_2DONAfWdzYhHy1KZ7-f4rI5WNuaXsKjRNoPW__5zF3ZK6xJdLbfDHqzJtA2t0tJEpRznbdh-qNFa1dOmSQMV-T5c9rNUA8Cq9dBgFhXoZpHNczRNUYR0baDpJoFGWaFzjKLZATwPbp_6d3bZUcEWStQKxRATSQ00yJnETkwl78kkor4MgogkUlBBnSQWScRjT7nZnk8SwpUCcwT2RMDwITTSLJVHgLDLHUmk8pYC7BPBGSE4cnyKOWM-l3EH3IqwoSjhxnXXi1lYAyUbQoWKUKEhVOh04Lz-Zr4E2_h1dLfiV1gKXh56gdK3DiaB34GLij-r1z_Pdvy34Sew5elCCJON1oVGsXiTp7Ah3otpvrCgeX07HD1asH5PbUvnk47VdUReLbNVPwAc6dqE |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1NT9wwEB0hqNT2AAVadflofYBTcev1R7w5IISgK9DCigNI3ELsOBLSKlk2oRV_it-Ix5vsCqRy49BbpCRW4hk_z9ie9wB2JMuND7NjGtsso7JrDE17pku15UiYljkd2yA2oYfD3vV1fLEAj20tDB6rbDExAHVWWlwj_8UjD6RMqEgejO8oqkbh7moroTF1i4F7-OtTtmr_9Njbd5fz_u_LoxPaqApQ692t9h8VdhMjJPpygmXamZ7LUy1dFKUqd1ZbzfLM5qnJuE81uVS5Mh7EmRXcRki-5CF_SYpehCNqoOkM-QUPkoR4RWPFdVOkE0r1MC7DWmhM3rUHGfZ8IpxHty82ZMM811_533roEyw3ETU5nA6BVVhwxRqsNNE1abCrWoOP5zOG2modfh6VBVLd-j4g_VFak-NJOa7IbUFSglWQQTeDXJQ1nqZKR5_h6k3-4QssFmXhvgIRXcOccj4vjIRU1sRKiZRJLUwcS-OyDnRbQya2IVZHfY9RMqOEDsZPvPGTYPyEdeDH7J3xlFbk1ae3WosnDcRUydzcHdhrfWZ--9-tbbze2nd4f3J5fpacnQ4Hm_CBY7lHOHO3BYv15N5twzv7p76tJt-C8xO4eWtfegJryTug |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3PT9swFH6qCkLbYUAZWscvH7YTy3DsOG4OCEFLBepWVWhIvWWx40hIVdI1GWj_2v46bNdpBRK9ceAWKT-U-H3-_F783vcAvgQ4E9rNjrxIpqkX-EJ4SUf4HpfECKalikfSNpvgw2FnPI5GDfhf18KYtMqaEy1Rp4U0_8hPSKiJFFMWBieZS4sY9fpn0z-e6SBldlrrdhpziAzUvwcdvpWn1z1t66-E9C9_da8812HAkxp6lX5Bu7MYGtEvRXHKleioLOGBCsOEZUpyyXGWyiwRKdFhJwlYxoQmdCwpkaERYtL0v8apDnqasHZxORzdLNYBSmyDQnPkRYxwV7JjC_eMl2Yqo00ozzXl4KfL4tLXfbY9a1e9_uZbHq8t-OB8bXQ-nxzb0FB5Czad340cq5UteP9zoV1b7sD3bpEbEVw9Hqg_SSrUmxXTEt3lKEGmPtJ21ECjojJ5VsnkI9y-yjfsQjMvcvUJEPUFVkzpiDGkAZMiYowmOOBURFEgVNoGvzZqLJ3kuun8MYkXYtEWCLEGQmyBEOM2HC_umc4FR1ZevV9bP3bkU8ZL07fhW42f5emXn_Z59dOOYENDKP5xPRzswTti6kBsMt4-NKvZX3UA6_K-uitnh24mIPj92mB6BIJqRfI |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Conducting+Flat+Drops+in+a+Confining+Potential&rft.jtitle=Archive+for+rational+mechanics+and+analysis&rft.au=Muratov%2C+Cyrill+B.&rft.au=Novaga%2C+Matteo&rft.au=Ruffini%2C+Berardo&rft.date=2022-03-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0003-9527&rft.eissn=1432-0673&rft.volume=243&rft.issue=3&rft.spage=1773&rft.epage=1810&rft_id=info:doi/10.1007%2Fs00205-021-01738-0&rft.externalDocID=10_1007_s00205_021_01738_0 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0003-9527&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0003-9527&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0003-9527&client=summon |