Lp REGULARITY OF LEAST GRADIENT FUNCTIONS

被引：1

作者：

Corny, Wojciech ^{[1
]}

机构：

[1] Univ Warsaw, Fac Math Informat & Mech, Warsaw, Poland

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 148卷 / 07期

关键词：

Least gradient problem; anisotropy; L-p regularity;

D O I：

10.1090/proc/15031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that in the anisotropic least gradient problem on an open bounded set Omega subset of R-N with Lipschitz boundary, given boundary data f is an element of L-p(partial derivative Omega) the solutions lie in LNp/N-1 (Omega); the exponent is shown to be optimal. Moreover, the solutions are shown to be locally bounded with explicit bounds on the rate of blow-up of the solution near the boundary in two settings: in the anisotropic case on the plane and in the isotropic case in any dimension.

引用

页码：3009 / 3019

页数：11

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