p-Harmonic mappings between metric spaces

被引：0

作者：

Guo, Chang-Yu ^{[1
,2
]}

Huang, Manzi ^{[3
]}

Wang, Zhuang ^{[3
]}

Xu, Haiqing ^{[1
,2
]}

机构：

[1] Shandong Univ, Res Ctr Math & Interdisciplinary Sci, Qingdao 266237, Peoples R China

[2] Minist Educ, Frontiers Sci Ctr Nonlinear Expectat, Qingdao, Peoples R China

[3] Hunan Normal Univ, Sch Math & Stat, MOE LCSM, Changsha 410081, Hunan, Peoples R China

来源：

MATHEMATISCHE ZEITSCHRIFT | 2022年 / 302卷 / 03期

关键词：

Metric valued Sobolev spaces; Dirichlet problem; Upper gradients; Hajlasz-Sobolev space; Trace operator; LIPSCHITZ CONTINUITY; SOBOLEV SPACES; MAPS; REGULARITY; TRACE; EXTENSION; THEOREMS;

D O I：

10.1007/s00209-022-03119-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we solve the Dirichlet problem for Sobolev maps between singular metric spaces that extends the corresponding result of Guo and Wenger (Commun Anal Geom 28(1):89-112, 2020). The main new ingredient in our proofs is a suitable extension of the theory of trace for metric valued Sobolev maps developed by Korevaar and Schoen (Commun Anal Geom 1(3-4):561-659, 1993) . We also develop a theory of trace in the borderline case, which investigates a sharp condition to characterize the existence of traces.

引用

页码：1797 / 1819

页数：23

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