The Dirichlet problem for Orlicz-Sobolev mappings between metric spaces

DOI10.1016/J.JMAA.2022.126730OpenAlexW4298008857MaRDI QIDQ2091039

Wen-Juan Qi

Publication date: 31 October 2022

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.00755

zbMATH Keywords

Dirichlet problemOrlicz-Sobolev spacesPoincaré inequalitytrace operatorRellich-Kondrachov compactness theorem

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)

Cites Work

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• Pointwise behaviour of Orlicz-Sobolev functions
• Quasiconformal maps in metric spaces with controlled geometry
• Hölder quasicontinuity of Sobolev functions on metric spaces
• Orlicz spaces and generalized Orlicz spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Sobolev spaces and harmonic maps for metric space targets
• Sobolev spaces on an arbitrary metric space
• Area minimizing discs in locally non-compact metric spaces
• Harmonic mappings between singular metric spaces
• Orlicz-Sobolev embeddings, extensions and Orlicz-Poincaré inequalities
• \(p\)-harmonic mappings between metric spaces
• Sharp self-improving properties of generalized Orlicz-Poincaré inequalities in connected metric measure spaces
• Strong and Weak Type Inequalities for Some Classical Operators in Orlicz Spaces
• Boundedness of solutions to variational problems under general growth conditions
• Sobolev Spaces on Metric Measure Spaces
• Harmonic functions on metric spaces

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