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
收藏
页码：1603 / 1648
页数：46
相关论文
共 50 条
12345