The Lin-Ni’s problem for mean convex domains

The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration...

Full description

Saved in:
Bibliographic Details
Main Authors: Druet, Olivier, Robert, Frédéric, Wei, Juncheng
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2011
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Blowing up (Algebraic geometry)
Convex domains
Differential equations, Elliptic
Neumann problem
Neumann elliptic problem
critical exponent
blow-up
ISBN:9780821869093, 0821869094
ISSN:0065-9266, 1947-6221
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.
AbstractList The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.
We prove some refined asymptotic estimates for positive blow-up solutions to
Author Wei, Juncheng
Robert, Frédéric
Druet, Olivier
Author_xml – sequence: 1
  fullname: Druet, Olivier
– sequence: 2
  fullname: Robert, Frédéric
– sequence: 3
  fullname: Wei, Juncheng
BackLink https://cir.nii.ac.jp/crid/1130000794356193408$$DView record in CiNii
BookMark eNpVkctOwzAQRc1TFOg3kAUSYmGYsWPHs4SKl1TBAsTWchJHBNIE6vJY8hv8Hl-C01YgvPDImqM7nnu32XrbtZ6xPYQjBILjWwCtOAmtuQBEHp-p5mqFDSkzYAQaAtRqlQ2Q0oxrIXDtr6cJSK6zwa_IBtuOMgIgE5husgEJQQa1VFtsGMIjxGOioqQBO7p78Mm4bvl1_f35FZLnaZc3fpJU3TSZeNcmRde--Y-k7CaubsMu26hcE_xwWXfY_fnZ3eiSj28urkYnY-4kpcbwyjmVgYASoMw8Co9IpXRGVOhK4bDIqwK9zl0hYi2kVk4T5WRUGVcqKrnDDhfCLjz59_DQNbNg3xqfd91TsP9ciezBgo2ff3n1YWbnWOHb2dQ19ux0JBFTqWUk9xdkW9e2qPsbUfZ-ZJRKpZFkCiZiuBw-CXY5EsH2Udl5VLZ32fZR2XlUVskfuC15lQ
CitedBy_id crossref_primary_10_1007_s00526_025_03035_0
crossref_primary_10_1007_s00208_024_02888_8
crossref_primary_10_1090_memo_1554
crossref_primary_10_1515_acv_2019_0023
crossref_primary_10_1007_s00526_014_0730_0
ContentType eBook
Book
Copyright Copyright 2011 American Mathematical Society
Copyright_xml – notice: Copyright 2011 American Mathematical Society
DBID RYH
DEWEY 515/.3533
DOI 10.1090/S0065-9266-2011-00646-5
DatabaseName CiNii Complete
DatabaseTitleList

DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISBN 9780821890165
0821890166
EISSN 1947-6221
Edition 1
ExternalDocumentID 9780821890165
EBC3114363
BB09540653
10_1090_S0065_9266_2011_00646_5
GroupedDBID --Z
-~X
123
4.4
6TJ
85S
AAFVP
ABPPZ
ACNCT
AEGFZ
AENEX
ALMA_UNASSIGNED_HOLDINGS
DU5
P2P
RMA
WH7
XOL
YNT
YQT
38.
50G
AABBV
AAWPO
ABARN
ABQPQ
ACLGV
ADVEM
AERYV
AFOJC
AHWGJ
AJFER
AZZ
BBABE
CZZ
GEOUK
RYH
ID FETCH-LOGICAL-a39488-faa57020d00d7e12e119d3a82f1ad2a1cbfc1e6bac2c1ec365a699b985d082cf3
ISBN 9780821869093
0821869094
ISICitedReferencesCount 23
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=0000050793&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0065-9266
IngestDate Fri Nov 08 05:34:41 EST 2024
Wed Nov 26 03:47:43 EST 2025
Thu Jun 26 21:09:21 EDT 2025
Thu Aug 14 15:25:06 EDT 2025
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Keywords Neumann elliptic problem
critical exponent
blow-up
LCCN 2012007214
LCCallNum_Ident QA374 .D784 2011
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-a39488-faa57020d00d7e12e119d3a82f1ad2a1cbfc1e6bac2c1ec365a699b985d082cf3
Notes "July 2012, volume 218, number 1027 (end of volume)"--T.p
Includes bibliography (p. 103-105)
OCLC 922981635
OpenAccessLink https://hal.science/hal-01279343
PQID EBC3114363
PageCount 118
ParticipantIDs askewsholts_vlebooks_9780821890165
proquest_ebookcentral_EBC3114363
nii_cinii_1130000794356193408
ams_ebooks_10_1090_S0065_9266_2011_00646_5
PublicationCentury 2000
PublicationDate c2011.
PublicationDateYYYYMMDD 2011-01-01
PublicationDate_xml – year: 2011
  text: c2011.
PublicationDecade 2010
PublicationPlace Providence, Rhode Island
PublicationPlace_xml – name: Providence, Rhode Island
– name: Providence, R.I
– name: Providence
PublicationSeriesTitle Memoirs of the American Mathematical Society
PublicationYear 2011
Publisher American Mathematical Society
Publisher_xml – name: American Mathematical Society
SSID ssj0000889039
ssj0008047
Score 2.58802
Snippet We prove some refined asymptotic estimates for positive blow-up solutions to
The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$,...
SourceID askewsholts
proquest
nii
ams
SourceType Aggregation Database
Publisher
SubjectTerms Blowing up (Algebraic geometry)
Convex domains
Differential equations, Elliptic
Neumann problem
TableOfContents Introduction -- <inline-formula content-type="math/mathml"> L ∞ − L^\infty - </inline-formula>bounded solutions -- Smooth domains and extensions of solutions to elliptic equations -- Exhaustion of the concentration points -- A first upper-estimate -- A sharp upper-estimate -- Asymptotic estimates in <inline-formula content-type="math/mathml"> C 1 ( Ω ) C^1\left (\Omega \right ) </inline-formula> -- Convergence to singular harmonic functions -- Estimates of the interior blow-up rates -- Estimates of the boundary blow-up rates -- Proof of Theorems and -- Construction and estimates on the Green’s function -- Projection of the test functions
Intro -- Contents -- Abstract -- Introduction -- Chapter 1. L-bounded solutions -- Chapter 2. Smooth domains and extensions of solutions to elliptic equations -- Chapter 3. Exhaustion of the concentration points -- Chapter 4. A first upper-estimate -- Chapter 5. A sharp upper-estimate -- Chapter 6. Asymptotic estimates in C1() -- Chapter 7. Convergence to singular harmonic functions -- 1. Convergence at general scale -- 2. Convergence at appropriate scale -- Chapter 8. Estimates of the interior blow-up rates -- Chapter 9. Estimates of the boundary blow-up rates -- Chapter 10. Proof of Theorems 1 and 2 -- Appendix A. Construction and estimates on the Green's function -- Appendix B. Projection of the test functions -- Bibliography
Title The Lin-Ni’s problem for mean convex domains
URI https://www.ams.org/memo/1027/
https://cir.nii.ac.jp/crid/1130000794356193408
https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=3114363
https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9780821890165&uid=none
Volume 218
WOSCitedRecordID wos0000050793&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
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1ba9RAFB7c1Qf3qd5waytBBEEdnGRym9ctWwVl60OVvg1zCwy2Wdlsy_58z1w2oxYRH3yZZALJJOdLcu7nIPSypUp3ymgMyoOzVskOC-AMuKSmoKp2OQm-zuynZrVqLy7Y59g7dPDtBJq-b3c79v2_Qg3HAGyXOvsPcI8XhQOwD6DDCLDD-JtEPE4T4qBa4pX1RvjYKsbHEV45e7sPMN-90esrYfvUT35zHfwRZ5fW8cjkgZExnec0etN12GysSu4cGzI7eoA-skCdTKK_WBCSa2gsFOsKkazHSiSjugnigu9gFXoa3vr5EkaC-7euMAPGj8NiIPTUuEr8ZowCXCxAvitdcdwJmjQ1qM533y_PvnwcbWQuBItQ5st2xpXLWDRpvJN9zB4j7_6wsq-hO8zQTAzfgHEAU9nCbNJbe4v_eqHi_ABNXaLJA3TH9A_RLJFleITeApZZwPLVkEUkM0Ayc0hmAcksIvkYfT1dnp98wLGvBRaUwQ8Td0JUDcjpmhDdmLwwec40FW3R5UIXIleyU7mppVAFbBWtK1EzJllbaXhw1dEnaNqve_MUZVoyrRtGTNvIkhRSgoTGCmmkIKYsSzNHr-Hhufe8DzxEHBDuKcUdpbijFPeU4tUcvfiJRvzmMp62JzhzuW9zdAyk48q6MXfeUBAzGUjdoIpT-ODnKNsTNSwbo4z5cnFCQfumNT38yyWeofvpPT1C0y18CcfonrrZ2mHzPL4lPwD2tknX
linkProvider ProQuest Ebooks
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%3Abook&rft.genre=book&rft.title=The+Lin-Ni%27s+problem+for+mean+convex+domains&rft.au=Druet%2C+Olivier&rft.au=Robert%2C+Fr%C3%A9d%C3%A9ric&rft.au=Wei%2C+Juncheng&rft.date=2011-01-01&rft.pub=American+Mathematical+Society&rft.isbn=9780821869093&rft_id=info:doi/10.1090%2FS0065-9266-2011-00646-5&rft.externalDocID=BB09540653
thumbnail_m http://cvtisr.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97808218%2F9780821890165.jpg