The Dirichlet Problem for Orlicz-Sobolev mappings between metric space
Functional Analysis
2021-12-30 v2 Classical Analysis and ODEs
Abstract
In this paper, we solve the Dirichlet problem for Orlicz-Sobolev maps between singular metric spaces that extends the corresponding result of Guo et al. [arXiv 2021]. As an intermediate step, we develop a version of Rellich-Kondrachov compactness theorem for Orlicz-Sobolev mappings between metric spaces that extends a previous result of Guo and Wenger [Comm. Anal. Geom. 2020]. Another crucial ingredient is an Orlicz-Sobolev extension of the trace theory for metric valued Sobolev maps developed by Korevaar and Schoen [Comm. Anal. Geom. 1993].
Keywords
Cite
@article{arxiv.2111.00755,
title = {The Dirichlet Problem for Orlicz-Sobolev mappings between metric space},
author = {Wen-Juan Qi},
journal= {arXiv preprint arXiv:2111.00755},
year = {2021}
}
Comments
25 pages. arXiv admin note: substantial text overlap with arXiv:2109.08436, arXiv:1701.06736 by other authors