The Relative Capacity

2008/06/09 by Markus Biegert, Biegert, Markus · 1 citation
Mathematics · #Analytic and geometric function theory #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0806.1417

Abstract

The purpose of this article is to introduce the relative p-capacity \Cap_p,Ω with respect to an open set Ω in \IR^N. It is a Choquet capacity on the closure of Ω and extends the classical p-capacity \Cap_p in the sense that \Cap_p,Ω=\Cap_p if Ω=\IR^N. The importance of the relative p-capacity stems from the fact that a large class of Sobolev functions defined on a 'bad domain' admit a trace on the boundary ∂Ω which is then unique up to \Cap_p,Ω-polar set. As an application we prove a characterization of W^1,p₀(Ω) for open sets Ω⊂\IR^N.

Citations

• Sobolev embeddings, extensions and measure density condition

Cited by

• Isometric Lattice Homomorphisms between Sobolev Spaces
• Lattice Homomorphisms between Sobolev Spaces

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