A problem of Baernstein on the equality of the 𝑝\mspace{1𝑚𝑢}-harmonic measure of a set and its closure

DOI10.1090/S0002-9939-05-08187-6zbMath1084.31008WikidataQ109994513 ScholiaQ109994513MaRDI QIDQ5705561

Nageswari Shanmugalingam, Anders Björn, Jana Björn

Publication date: 9 November 2005

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceLipschitz domainstarshaped domainDirichlet problem for \(p\)-harmonic functions

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Capacity and harmonic measure in the complex plane (30C85) Potentials and capacities on other spaces (31C15) Other generalizations (nonlinear potential theory, etc.) (31C45) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

Related Items

Unnamed Item ⋮ Estimates for nonlinear harmonic measures on trees ⋮ \(p\)-harmonic functions with boundary data having jump discontinuities and Baernstein's problem ⋮ The Dirichlet problem for \(p\)-harmonic functions on the topologist's comb

Cites Work

• Traces of Sobolev functions on fractal type sets and characterization of extension domains
• The Perron method for \(p\)-harmonic functions in metric spaces.
• p-Harmonic Functions in the Plane
• Weakly Differentiable Functions
• The Dirichlet problem for p-harmonic functions on metric spaces
• Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A problem of Baernstein on the equality of the 𝑝\mspace{1𝑚𝑢}-harmonic measure of a set and its closure