Notions of Dirichlet problem for functions of least gradient in metric measure spaces

被引：13

作者：

Korte, Riikka ^{[1
]}

Lahti, Panu ^{[2
,3
]}

Li, Xining ^{[4
]}

Shanmugalingam, Nageswari ^{[2
]}

机构：

[1] Aalto Univ, Dept Math & Syst Anal, POB 11100, Aalto 00076, Finland

[2] Univ Cincinnati, Dept Math Sci, POB 210025, Cincinnati, OH 45221 USA

[3] Univ Jyvaskyla, Dept Math & Stat, POB 35, Jyvaskyla 40014, Finland

[4] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2019年 / 35卷 / 06期

基金：

芬兰科学院;

关键词：

Function of bounded variation; inner trace; perimeter; least gradient; p-liarmonic; Dirichlet problem; metric measure space; Poincare inequality; codimension 1 Hausdorff measure; BOUNDED VARIATION; FINITE PERIMETER; LIPSCHITZ FUNCTIONS; HARMONIC-FUNCTIONS; SETS; APPROXIMATION; CAPACITIES;

D O I：

10.4171/RMI/1095

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincare inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazon-Rossi-De Leon, solutions by considering the Dirichlet problem for p-harrnonic functions, p > 1, and letting p -> 1. Tools developed and used in this paper include the inner perimeter measure of a domain.

引用

页码：1603 / 1648

页数：46

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