Uniqueness of bubbling solutions of mean field equations

doi:10.1016/j.matpur.2018.12.002

	Uniqueness of bubbling solutions of mean field equations
	Yang, Wen 1; Lee, Youngae 2; Jevnikar, Aleks 3; Bartolucci, Daniele 4
刊名	JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
	2019-03-01
卷号	123 页码:78-126
关键词	Lionville-type equations Mean field equations Bubbling solutions Uniqueness results
ISSN号	0021-7824
DOI	10.1016/j.matpur.2018.12.002
英文摘要	We prove the uniqueness of blow up solutions of the mean field equation as rho(n) -> 8 pi m, m is an element of N. If u(n,1) and u(n,2) are two sequences of bubbling solutions with the same rho(n), and the same (non degenerate) blow up set, then u(n,1) = u(n,2) for sufficiently large n. The proof of the uniqueness requires a careful use of some sharp estimates for bubbling solutions of mean field equations [22] and a rather involved analysis of suitably defined Pohozaev-type identities as recently developed in [51] in the context of the Chern-Simons-Higgs equations. Moreover, motivated by the Onsager statistical description of two dimensional turbulence, we are bound to obtain a refined version of an estimate about rho(n) - 8 pi m in case the first order evaluated in [22] vanishes. (C) 2019 Elsevier Masson SAS. All rights reserved.
资助项目	FIRB project "Analysis and Beyond" ; PRIN project 2015, "Variational methods, with applications to problems in mathematical physics and geometry" ; Consolidate the Foundations project 2015 ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program[Y8Y3011001] ; NSFC[11801550]
WOS关键词	BLOW-UP ANALYSIS ; LIOUVILLE-TYPE ; ELLIPTIC EQUATION ; SINGULAR LIMITS ; NON-DEGENERACY ; INEQUALITY ; EXISTENCE ; CURVATURE ; SURFACES ; BEHAVIOR
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE BV
WOS记录号	WOS:000459846200003
资助机构	FIRB project "Analysis and Beyond" ; FIRB project "Analysis and Beyond" ; PRIN project 2015, "Variational methods, with applications to problems in mathematical physics and geometry" ; PRIN project 2015, "Variational methods, with applications to problems in mathematical physics and geometry" ; Consolidate the Foundations project 2015 ; Consolidate the Foundations project 2015 ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; FIRB project "Analysis and Beyond" ; FIRB project "Analysis and Beyond" ; PRIN project 2015, "Variational methods, with applications to problems in mathematical physics and geometry" ; PRIN project 2015, "Variational methods, with applications to problems in mathematical physics and geometry" ; Consolidate the Foundations project 2015 ; Consolidate the Foundations project 2015 ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; FIRB project "Analysis and Beyond" ; FIRB project "Analysis and Beyond" ; PRIN project 2015, "Variational methods, with applications to problems in mathematical physics and geometry" ; PRIN project 2015, "Variational methods, with applications to problems in mathematical physics and geometry" ; Consolidate the Foundations project 2015 ; Consolidate the Foundations project 2015 ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; FIRB project "Analysis and Beyond" ; FIRB project "Analysis and Beyond" ; PRIN project 2015, "Variational methods, with applications to problems in mathematical physics and geometry" ; PRIN project 2015, "Variational methods, with applications to problems in mathematical physics and geometry" ; Consolidate the Foundations project 2015 ; Consolidate the Foundations project 2015 ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/14217]
专题	中国科学院武汉物理与数学研究所
通讯作者	Bartolucci, Daniele
作者单位	1.Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Hubei, Peoples R China 2.Kyungpook Natl Univ, Teachers Coll, Dept Math Educ, Daegu, South Korea 3.Univ Pisa, Dept Math, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy 4.Univ Roma Tor Vergata, Dept Math, Via Ric Sci 1, I-00133 Rome, Italy
推荐引用方式 GB/T 7714	Yang, Wen,Lee, Youngae,Jevnikar, Aleks,et al. Uniqueness of bubbling solutions of mean field equations[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,2019,123:78-126.
APA	Yang, Wen,Lee, Youngae,Jevnikar, Aleks,&Bartolucci, Daniele.(2019).Uniqueness of bubbling solutions of mean field equations.JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,123,78-126.
MLA	Yang, Wen,et al."Uniqueness of bubbling solutions of mean field equations".JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 123(2019):78-126.