The Liouville theorem for \(p\)-harmonic functions and quasiminimizers with finite energy

DOI10.1007/s00209-020-02536-2zbMath1456.35055arXiv1809.07155OpenAlexW3038107134WikidataQ109994272 ScholiaQ109994272MaRDI QIDQ2223536

Jana Björn, Nageswari Shanmugalingam, Anders Björn

Publication date: 29 January 2021

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.07155

zbMATH Keywords

Poincaré inequalitydoubling measureweak maximum principlemetric measure space\(p\)-harmonic functionquasiminimizerfinite \(p\)-energyquasiharmonic functionannular quasiconvexity

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Variational methods for second-order elliptic equations (35J20) Other generalizations (nonlinear potential theory, etc.) (31C45) Cluster sets, prime ends, boundary behavior (30D40) Quasilinear elliptic equations with (p)-Laplacian (35J92) Potential theory on fractals and metric spaces (31E05) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53) Inequalities in metric spaces (30L15) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Related Items (6)

Gradient estimates for weighted \(p\)-Laplacian equations on Riemannian manifolds with a Sobolev inequality and integral Ricci bounds ⋮ Removable singularities for bounded \(\mathcal{A} \)-(super)harmonic and quasi(super)harmonic functions on weighted \(\mathbf{R}^n\) ⋮ Corrigendum to: ``Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces ⋮ Classification of metric measure spaces and their ends using p-harmonic functions ⋮ \(p\)-hyperbolicity of ends and families of paths in metric spaces ⋮ Bounded geometry and \(p\)-harmonic functions under uniformization and hyperbolization

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