ON A FRACTIONAL VERSION OF A MURAT COMPACTNESS RESULT AND APPLICATIONS

被引：3

作者：

Antil, Harbir ^{[1
,2
]}

Rautenberg, Carlos N. ^{[1
,2
]}

Schikorra, Armin ^{[3
]}

机构：

[1] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA

[2] George Mason Univ, Ctr Math & Artificial Intelligence CMAI, Fairfax, VA 22030 USA

[3] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15261 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2021年 / 53卷 / 03期

关键词：

Murat and Brezis; fractional Sobolev spaces; compactness; Mosco convergence; Boccardo and Murat; QUASI-VARIATIONAL INEQUALITY; EVERYWHERE CONVERGENCE; GRADIENTS; SANDPILES;

D O I：

10.1137/20M1379873

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper provides an extension to fractional order Sobolev spaces of the classical result of Murat and Brezis which states that the cone of positive elements in H-1(Omega) compactly embeds in W--1,W-q(Omega) for every q < 2 and for any open and bounded set Omega with Lipschitz boundary. In particular, our proof contains the classical result. Several new analysis tools are developed during the course of the proof to our main result which are of wider interest. Subsequently, we apply our results to the convergence of convex sets and establish a fractional version of the Mosco convergence result of Boccardo and Murat. We conclude with an application of this result to quasi-variational inequalities.

引用

页码：3158 / 3187

页数：30

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