Resolutivity and invariance for the Perron method for degenerate equations of divergence type

DOI10.1016/j.jmaa.2021.125937zbMath1483.35097arXiv2008.00883OpenAlexW3046272986MaRDI QIDQ2069781

Jana Björn, Anders Björn, Abubakar Mwasa

Publication date: 21 January 2022

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

Full work available at URL: https://arxiv.org/abs/2008.00883

zbMATH Keywords

Dirichlet problemdegenerate quasilinear elliptic equationPerron solutions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Degenerate elliptic equations (35J70) Quasilinear elliptic equations (35J62)

Related Items (1)

Volume growth, capacity estimates, \(p\)-parabolicity and sharp integrability properties of \(p\)-harmonic Green functions

Cites Work

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• Nonlinear potential theory on metric spaces
• Two theorems of N. Wiener for solutions of quasilinear elliptic equations
• Note on the PWB-method in the nonlinear case
• The Perron method for \(p\)-harmonic functions in metric spaces.
• The Perron method for \(p\)-harmonic functions in unbounded sets in \(\mathbf {R}^n\) and metric spaces
• The Dirichlet problem for \(p\)-harmonic functions with respect to arbitrary compactifications
• The Dirichlet problem for \(p\)-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities
• The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in R^n and metric spaces

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