Necessity of a Wiener type condition for boundary regularity of quasiminimizers and nonlinear elliptic equations

DOI10.1007/s00526-008-0216-zzbMath1177.31007OpenAlexW2135574970MaRDI QIDQ834621

Jana Björn

Publication date: 27 August 2009

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-008-0216-z

zbMATH Keywords

boundary regularity\(p\)-harmonic functions\(p\)-energy integral

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Regularity of solutions in optimal control (49N60) A priori estimates in context of PDEs (35B45) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (7)

Sharp exponents and a Wiener type condition for boundary regularity of quasiminimizers ⋮ Sphericalization and \(p\)-harmonic functions on unbounded domains in Ahlfors regular spaces ⋮ BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers ⋮ The variational capacity with respect to nonopen sets in metric spaces ⋮ The Kellogg property and boundary regularity forp-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications ⋮ Boundary regularity for p-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces ⋮ Minima of quasisuperminimizers

Cites Work

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• A weak Kellogg property for quasiminimizers
• Boundary regularity for \(p\)-harmonic functions and solutions of the obstacle problem on metric spaces
• Boundary regularity for quasiminima
• A regularity condition at the boundary for solutions of quasilinear elliptic equations
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• The Wiener test and potential estimates for quasilinear elliptic equations
• The Perron method for \(p\)-harmonic functions in metric spaces.
• Fat sets and pointwise boundary estimates for \(p\)-harmonic functions in metric spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Boundary continuity for quasiminimizers on metric spaces
• Nonlinear potential theory of metric spaces
• The Poincaré inequality is an open ended condition
• A regularity classification of boundary points for \(p\)-harmonic functions and quasiminimizers
• Fine continuity on metric spaces
• Nonsmooth calculus
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• The Dirichlet problem for p-harmonic functions on metric spaces
• Regularity at the boundary for solutions of nonlinear subelliptic equations
• Regularity of quasi-minimizers on metric spaces
• Harmonic functions on metric spaces

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