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.

引用

页码：211 / 223

页数：13

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