Liouville equations from a variational point of view

被引：0
|
作者：
Malchiodi, Andrea [1 ,2 ]
机构：
[1] SISSA, Via Bonomea 265, I-34136 Trieste, Italy
[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England
来源：
PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL III | 2014年
关键词：
Liouville equations; variational methods; conformal geometry; singular PDEs; BLOW-UP ANALYSIS; STATISTICAL-MECHANICS; CONFORMAL METRICS; COMPACT SURFACES; Q-CURVATURE; EXISTENCE; INEQUALITY; SYMMETRY; SOBOLEV; THEOREM;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
After discussing the role of Liouville equations in both Conformal Geometry and Mathematical Physics, we will explore some of their variational features. In particular we will show the role of the Moser-Trudinger inequality, as well as of some of its improved versions, in characterizing the Euler-Lagrange energy levels of the problems under interest. This description reduces the study of PDEs of Liouville type to topological properties of explicit finite-dimensional objects.
引用
收藏
页码：345 / 361
页数：17
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