The Dirichlet Problem for Orlicz-Sobolev mappings between metric space

DOI10.1016/J.JMAA.2022.126730arXiv2111.00755MaRDI QIDQ6381832

Publication date: 1 November 2021

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].

Mathematics Subject Classification ID

Elliptic equations and elliptic systems (35J99) Potential theory on fractals and metric spaces (31E05) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

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