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A mean field equation involving positively supported probability measures: blow-up phenomena and variational aspects
Jevnikar, Aleks1; Yang, Wen2
2019-04-01
Source PublicationPROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN0308-2105
Volume149Issue:2Pages:325-352
AbstractWe are concerned with an elliptic problem which describes a mean field equation of the equilibrium turbulence of vortices with variable intensities. In the first part of the paper, we describe the blow-up picture and highlight the differences from the standard mean field equation as we observe non-quantization phenomenon. In the second part, we discuss the Moser-Trudinger inequality in terms of the blow-up masses and get the existence of solutions in a non-coercive regime by means of a variational argument, which is based on some improved Moser-Trudinger inequalities.
Keywordgeometric PDEs mean field equation blow-up analysis variational methods
Funding OrganizationPRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; FIRB project: Analysis and Beyond ; FIRB project: Analysis and Beyond ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; FIRB project: Analysis and Beyond ; FIRB project: Analysis and Beyond ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; FIRB project: Analysis and Beyond ; FIRB project: Analysis and Beyond ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; FIRB project: Analysis and Beyond ; FIRB project: Analysis and Beyond ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program
DOI10.1017/prm.2018.30
WOS KeywordSCALAR-CURVATURE ; EXISTENCE RESULT ; STATISTICAL-MECHANICS ; VARIABLE INTENSITIES ; ELLIPTIC EQUATION ; COMPACT SURFACES ; TODA SYSTEM ; CLASSIFICATION ; LIMITS ; FLOWS
Language英语
Funding ProjectPRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; FIRB project: Analysis and Beyond ; CAS Pioneer Hundred Talents Program
Funding OrganizationPRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; FIRB project: Analysis and Beyond ; FIRB project: Analysis and Beyond ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; FIRB project: Analysis and Beyond ; FIRB project: Analysis and Beyond ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; FIRB project: Analysis and Beyond ; FIRB project: Analysis and Beyond ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems ; FIRB project: Analysis and Beyond ; FIRB project: Analysis and Beyond ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000464008500004
PublisherCAMBRIDGE UNIV PRESS
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.apm.ac.cn/handle/112942/13767
Collection中国科学院武汉物理与数学研究所
Corresponding AuthorJevnikar, Aleks
Affiliation1.Univ Pisa, Dept Math, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy
2.Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Hubei, Peoples R China
Recommended Citation
GB/T 7714
Jevnikar, Aleks,Yang, Wen. A mean field equation involving positively supported probability measures: blow-up phenomena and variational aspects[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,2019,149(2):325-352.
APA Jevnikar, Aleks,&Yang, Wen.(2019).A mean field equation involving positively supported probability measures: blow-up phenomena and variational aspects.PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,149(2),325-352.
MLA Jevnikar, Aleks,et al."A mean field equation involving positively supported probability measures: blow-up phenomena and variational aspects".PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS 149.2(2019):325-352.
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