Inverse boundary-value problems of cauchy type for harmonic functions
We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown curve Γ. We obtain criteria for Γ to be the unit circle. We apply the proposed methods for solving a modified Hadamard example and generaliz...
Saved in:
| Published in: | Russian mathematics Vol. 56; no. 12; pp. 71 - 75 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Heidelberg
Allerton Press, Inc
01.12.2012
|
| Subjects: | |
| ISSN: | 1066-369X, 1934-810X |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown curve Γ. We obtain criteria for Γ to be the unit circle. We apply the proposed methods for solving a modified Hadamard example and generalize the obtained results for the case of doubly connected domains. |
|---|---|
| AbstractList | We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown curve Γ. We obtain criteria for Γ to be the unit circle. We apply the proposed methods for solving a modified Hadamard example and generalize the obtained results for the case of doubly connected domains. |
| Author | Aksent’ev, L. A. Abubakirov, N. R. |
| Author_xml | – sequence: 1 givenname: N. R. surname: Abubakirov fullname: Abubakirov, N. R. email: Nail.Abubakirov@ksu.ru organization: Kazan (Volga Region) Federal University – sequence: 2 givenname: L. A. surname: Aksent’ev fullname: Aksent’ev, L. A. organization: Kazan (Volga Region) Federal University |
| BookMark | eNp9kEFrAjEQhUOxULX9Ab3lD2w7k8SsORaxrSD00Ba8LdnZpK5oIokr-O-7ordCT2_gzfd4vBEbhBgcY48ITxJBPn8iaC21WaFAATCFGzZEI1UxRVgN-ru3i7N_x0Y5bwAmWig9ZPNFOLqUHa9jFxqbTsXRbjvH9ynWW7fLPHpOtqP1iR9Oe8d9THxt0y6GlrjvAh3aGPI9u_V2m93DVcfs-3X-NXsvlh9vi9nLsiCh4FBo2zQ0RaptCajKWnorjKSJ0aUhr1E3QjYOQQktJgZrTcIZRUJYowA1yTHDSy6lmHNyvtqndte3rhCq8w7Vnx16RlyY3P-GH5eqTexS6Gv-A_0CxEBhsA |
| Cites_doi | 10.4213/mzm8553 |
| ContentType | Journal Article |
| Copyright | Allerton Press, Inc. 2012 |
| Copyright_xml | – notice: Allerton Press, Inc. 2012 |
| DBID | AAYXX CITATION |
| DOI | 10.3103/S1066369X12120080 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1934-810X |
| EndPage | 75 |
| ExternalDocumentID | 10_3103_S1066369X12120080 |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 123 1N0 29P 2J2 2JN 2JY 2KG 2LR 2~H 30V 4.4 408 40D 40E 5VS 6NX 78A 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAYIU AAYQN AAYTO AAYZH ABAKF ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACCUX ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADRFC ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AEOHA AEPYU AETLH AEVLU AEXYK AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ AXYYD B-. BA0 BAPOH BDATZ BGNMA CAG COF CS3 DDRTE DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 H13 HF~ HG6 HLICF HMJXF HRMNR HZ~ IJ- IKXTQ IWAJR I~X I~Z J-C JBSCW JZLTJ KOV LLZTM M4Y MA- NB0 NPVJJ NQJWS NU0 O9- O93 O9J P9R PF0 PT4 QOS R89 R9I RIG RNS ROL RPX RSV S16 S1Z S27 S3B SAP SDH SHX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W48 WK8 XU3 YLTOR ZMTXR ~A9 AAPKM AAYXX ABDBE ABFSG ABJCF ABRTQ ACSTC AEZWR AFDZB AFFHD AFHIU AFKRA AFOHR AHPBZ AHWEU AIXLP ATHPR AZQEC BENPR BGLVJ CCPQU CITATION DWQXO GNUQQ HCIFZ M2P M7S PHGZM PHGZT PQGLB PTHSS |
| ID | FETCH-LOGICAL-c240t-6addc81cba70147b3fa293c59679cf616d23de104262591b6c2e94c22a94016c3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000439486500008&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1066-369X |
| IngestDate | Sat Nov 29 05:49:34 EST 2025 Fri Feb 21 02:34:23 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 12 |
| Keywords | inverse boundary-value problems boundary-value problems for analytic functions harmonic functions Cauchy problem |
| Language | English |
| License | http://www.springer.com/tdm |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c240t-6addc81cba70147b3fa293c59679cf616d23de104262591b6c2e94c22a94016c3 |
| PageCount | 5 |
| ParticipantIDs | crossref_primary_10_3103_S1066369X12120080 springer_journals_10_3103_S1066369X12120080 |
| PublicationCentury | 2000 |
| PublicationDate | 20121200 2012-12-00 |
| PublicationDateYYYYMMDD | 2012-12-01 |
| PublicationDate_xml | – month: 12 year: 2012 text: 20121200 |
| PublicationDecade | 2010 |
| PublicationPlace | Heidelberg |
| PublicationPlace_xml | – name: Heidelberg |
| PublicationTitle | Russian mathematics |
| PublicationTitleAbbrev | Russ Math |
| PublicationYear | 2012 |
| Publisher | Allerton Press, Inc |
| Publisher_xml | – name: Allerton Press, Inc |
| References | Demtchenko (CR2) 1929; 189 Gahov (CR5) 1977 Tumashev, Nuzhin (CR3) 1965 Demidov, Platushchikhin (CR1) 2010; 87 Petrovskii (CR4) 1961 G. G. Tumashev (9444_CR3) 1965 I. A. Petrovskii (9444_CR4) 1961 F. D. Gahov (9444_CR5) 1977 B. Demtchenko (9444_CR2) 1929; 189 A. S. Demidov (9444_CR1) 2010; 87 |
| References_xml | – volume: 189 start-page: 725 year: 1929 end-page: 726 ident: CR2 article-title: Sur un Probleme Inverse au Probleme de Dirichlet publication-title: Compt. Rend. Acad. Sci. Paris – volume: 87 start-page: 141 issue: 1 year: 2010 end-page: 143 ident: CR1 article-title: Explicit Formula for the Gradient of a Harmonic Function from Its Analytic Cauchy Data on the Analytic Curve publication-title: Matem. Zametki doi: 10.4213/mzm8553 – year: 1961 ident: CR4 publication-title: Lectures on Partial Differential Equations – year: 1965 ident: CR3 publication-title: Inverse Boundary-Value Problems with Applications – year: 1977 ident: CR5 publication-title: Boundary-Value Problems – volume: 87 start-page: 141 issue: 1 year: 2010 ident: 9444_CR1 publication-title: Matem. Zametki doi: 10.4213/mzm8553 – volume-title: Inverse Boundary-Value Problems with Applications year: 1965 ident: 9444_CR3 – volume: 189 start-page: 725 year: 1929 ident: 9444_CR2 publication-title: Compt. Rend. Acad. Sci. Paris – volume-title: Boundary-Value Problems year: 1977 ident: 9444_CR5 – volume-title: Lectures on Partial Differential Equations year: 1961 ident: 9444_CR4 |
| SSID | ssj0056246 |
| Score | 1.832045 |
| Snippet | We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown... |
| SourceID | crossref springer |
| SourceType | Index Database Publisher |
| StartPage | 71 |
| SubjectTerms | Brief Communications Mathematics Mathematics and Statistics |
| Title | Inverse boundary-value problems of cauchy type for harmonic functions |
| URI | https://link.springer.com/article/10.3103/S1066369X12120080 |
| Volume | 56 |
| WOSCitedRecordID | wos000439486500008&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 1997-Present customDbUrl: eissn: 1934-810X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0056246 issn: 1066-369X databaseCode: RSV dateStart: 20070101 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/eLvHCXMwnV09T8MwED1BYYCBb0T5kgcmkEXsOE48ItSKASpEoeoW2a4tWFKUtEj999hOglQBA-ynKDqd773znd8BXHDrZd5iPxRGBGYmYVixlOJIZkKJSFId5JpG9-lgkI3H4rF5x1210-5tSzJk6lBXRvH1kHh05GJMXLb1RGcV1hzaZf40Pg1Hbfp1eF4_KXLW2JvXrcyfP7EMRsud0AAw_e1__doObDV8Et3UAbALK6bYg82HLzHWah96XkujrAxSYYVSucBe4dugZpdMhaYWaTnXrwvkL2SRo7HIC1p70VzkcS-E5gG89HvPt3e42Z6AtUPpGeYuc-mMaCVTVwalKrbSQbtOBE-FtpzwCY0nhgRJ-kQQxTU1gmlKpXA1F9fxIXSKaWGOAFlhuRXSJlxLpiIqJhGTmtHUsS1FVdSFy9aN-XstkpG74sL7Jv_mmy5ctU7Mm_NS_W59_CfrE9hwhIbW4yan0JmVc3MG6_pj9laV5yFOPgFlQbVT |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NSwMxEB20CurBb7F-5uBJCe5ms9nmKNJSsS1ia-ltSdIEvbSy2wr99ybZXaGoB70PSxgm897sTN4AXDHjZN4iNxQWckx1TLGkCcGBaHDJA0GUl2sadpJerzEa8afyHXdeTbtXLUmfqX1dGUS3_dChI-Oj0GZbR3RWYY1awHJzfM_9YZV-LZ4XT4qsNXbmRSvz508sg9FyJ9QDTGvnX0fbhe2ST6K7IgD2YEVP9mGr-yXGmh9A02lpZLlG0q9QyhbYKXxrVO6SydHUICXm6nWB3A9ZZGkscoLWTjQXOdzzoXkIL63m4L6Ny-0JWFmUnmFmM5dqhEqKxJZBiYyMsNCuYs4SrgwL2ZhEYx16SfqYh5IpojlVhAhuay6moiOoTaYTfQzIcMMMFyZmSlAZED4OqFCUJJZtSSKDOlxXbkzfC5GM1BYXzjfpN9_U4aZyYlrel_x365M_WV_CRnvQ7aSdh97jKWxackOK0ZMzqM2yuT6HdfUxe8uzCx8zn_C2uDc |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LSwMxEB60iujBt1ifOXhSQnez2WxzFG1RrKVQLb0tSZqgl23Z3Qr99yb7EIp6EO_DEobJfDM7k-8DuGLG0bwFbinM55jqkGJJI4I90eaSe4Kogq5p1Iv6_fZ4zAeVzmlWb7vXI8nyTYNjaUry1mxiWkWP6QWtoe-QkvGxbzOvK3pWYY06zSDXrg9HdSq22F4-L7LW2JmXY82fP7EMTMtT0QJsujv_PuYubFd1JrotA2MPVnSyD1vPXySt2QF0HMdGmmkkC2mldIEd87dGlcZMhqYGKTFXbwvkftQiW94iR3TtyHSRw8MiZA_htdt5uXvAlaoCVha9c8xsRlNtX0kR2fYokoERFvJVyFnElWE-m5Bgov2Cqj7kvmSKaE4VIYLbXoyp4AgayTTRx4AMN8xwYUKmBJUe4ROPCkVJZKswSaTXhOvapfGsJM-IbdPhfBN_800TbmqHxtU9yn63PvmT9SVsDO67ce-x_3QKm7bmIeVGyhk08nSuz2FdfeTvWXpRhM8nSa_BGw |
| 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=Inverse+boundary-value+problems+of+cauchy+type+for+harmonic+functions&rft.jtitle=Russian+mathematics&rft.au=Abubakirov%2C+N.+R.&rft.au=Aksent%E2%80%99ev%2C+L.+A.&rft.date=2012-12-01&rft.pub=Allerton+Press%2C+Inc&rft.issn=1066-369X&rft.eissn=1934-810X&rft.volume=56&rft.issue=12&rft.spage=71&rft.epage=75&rft_id=info:doi/10.3103%2FS1066369X12120080&rft.externalDocID=10_3103_S1066369X12120080 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1066-369X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1066-369X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1066-369X&client=summon |