English

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

R2 v1 2026-06-24T07:20:26.879Z