Cluster sets for Sobolev functions and quasiminimizers

DOI10.1007/s11854-010-0025-0zbMath1223.31005OpenAlexW1994341497MaRDI QIDQ628362

Anders Björn

Publication date: 10 March 2011

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-010-0025-0

zbMATH Keywords

capacityupper gradient\((1,q)\)-Poincaré inequalityquasiharmonic functionrefined Sobolev space

Mathematics Subject Classification ID

Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (9)

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 ⋮ \(p\)-harmonic functions with boundary data having jump discontinuities and Baernstein's problem ⋮ Boundary regularity for p-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces ⋮ Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology ⋮ Minima of quasisuperminimizers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear potential theory on metric spaces
• Quasi-minima
• Pasting lemmas and characterizations of boundary regularity for quasiminimizers
• A weak Kellogg property for quasiminimizers
• Regularity in capacity and the Dirichlet Laplacian
• Boundary regularity for \(p\)-harmonic functions and solutions of the obstacle problem on metric spaces
• Moser iteration for (quasi)minimizers on metric spaces
• Boundary regularity for quasiminima
• On the regularity of the minima of variational integrals
• 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 Perron method 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
• Sobolev spaces with zero boundary values on metric spaces
• The Poincaré inequality is an open ended condition
• Weak barriers in nonlinear potential theory
• A regularity classification of boundary points for \(p\)-harmonic functions and quasiminimizers
• Nonlinear ground states in irregular domains
• The Dirichlet problem for p-harmonic functions on metric spaces
• Regularity of quasi-minimizers on metric spaces
• Harmonic functions on metric spaces

This page was built for publication: Cluster sets for Sobolev functions and quasiminimizers