Gradient stability for the Sobolev inequality: the case p ≥ 2

被引：30

作者：

Figalli, Alessio ^{[1
]}

Neumayer, Robin ^{[2
]}

机构：

[1] Swiss Fed Inst Technol, Dept Math, HG G 63-2,Ramistr 101, CH-8092 Zurich, Switzerland

[2] Northwestern Univ, Dept Math, 2033 Sheridan Rd, Evanston, IL 60208 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2019年 / 21卷 / 02期

关键词：

Sobolev inequality; stability; quantitative inequalities; ISOPERIMETRIC PROBLEM; SHARP SOBOLEV; THEOREMS;

D O I：

10.4171/JEMS/837

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a strong form of the quantitative Sobolev inequality in R-n for p >= 2, where the deficit of a function u is an element of (W)over dot(1, p) controls parallel to del u - del v parallel to(Lp) for an extremal function v in the Sobolev inequality.

引用

页码：319 / 354

页数：36

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