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.
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页码：1797 / 1819
页数：23
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