A variational proof of Nash's inequality

被引：4
|
作者：
Bouin, Emeric [1 ,2 ]
Dolbeault, Jean [1 ,2 ]
Schmeiser, Christian [3 ]
机构：
[1] CNRS, UMR 7534, CEREMADE, Pl Lattre de Tassigny, F-75775 Paris 16, France
[2] PSL Res Univ, Univ Paris Dauphine, Pl Lattre de Tassigny, F-75775 Paris 16, France
[3] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
来源：
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2020年 / 31卷 / 01期
关键词：
Nash inequality; interpolation; semi-linear elliptic equations; compactness; compact support; Neumann homogeneous boundary conditions; Laplacian; radial symmetry; COMPACT SUPPORT; UNIQUENESS; EXISTENCE; EQUATIONS;
D O I：
10.4171/RLM/886
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is intended to give a characterization of the optimality case in Nash's inequality, based on methods of nonlinear analysis for elliptic equations and techniques of the calculus of variations. By embedding the problem into a family of Gagliardo-Nirenberg inequalities, this approach reveals why optimal functions have compact support and also why optimal constants are determined by a simple spectral problem.
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页码：211 / 223
页数：13
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