Matrix Ap Weights, Degenerate Sobolev Spaces, and Mappings of Finite Distortion

被引：0

作者：

Cruz-Uribe, David ^{[1
]}

Moen, Kabe ^{[1
]}

Rodney, Scott ^{[2
]}

机构：

[1] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

[2] Cape Breton Univ, Dept Math Phys & Geol, Sydney, NS B1P6L2, Canada

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2016年 / 26卷 / 04期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

Matrix A(p); Degenerate Sobolev spaces; Mappings of finite distortion; MAXIMAL FUNCTIONS; WEAK SOLUTIONS; BESOV-SPACES; EQUATIONS; INEQUALITIES; REGULARITY; BASES;

D O I：

10.1007/s12220-015-9649-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study degenerate Sobolev spaces where the degeneracy is controlled by a matrix weight. This class of weights was introduced by Nazarov, Treil and Volberg, and degenerate Sobolev spaces with matrix weights have been considered by several authors for their applications to PDEs. We prove that the classical Meyers-Serrin theorem, , holds in this setting. As applications we prove partial regularity results for weak solutions of degenerate p-Laplacian equations, and in particular for mappings of finite distortion.

引用

页码：2797 / 2830

页数：34

共 39 条

[11] Vector A2 weights and a Hardy-Littlewood maximal function [J].