Some properties of a class of nonlinear variational \(\mu\)-capacities
type: Item
instance of: scholarly article
title: Some properties of a class of nonlinear variational \(\mu\)-capacities
zbMATH Open document ID: 0657.49006
DOI: 10.1016/0022-1236(88)90022-5
author: G. Dal Maso
author: Anneliese Defranceschi
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: This paper deals with a class of Borel measures \(\mu\) such that \(\mu (B)=0\) for every Borel subset B belonging to the \(\sigma\)-field B(\(\Omega)\). This class of measures is denoted by \(M_ p(\Omega)\). For every \(\mu\) belonging to \(M_ p(\Omega)\) and B belonging to B(\(\Omega)\), the \(\mu\)-capacity of B, relative to a function f(x,\(\delta)\) (which is Lebesgue measurable in x and convex in \(\delta)\), is defined. The main result of this paper is an explicit formula which permits to reconstruct a measure \(\mu\) of \(M_ p(\Omega)\) from the corresponding \(\mu\)-capacity relative to f(x,\(\delta)\). The result is closely related to the study of limits of solutions of non-linear Dirichlet problems in open sets with holes.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 31B15
zbMATH DE Number: 4073826
zbMATH Keywords: \(\mu\)-capacity
zbMATH Keywords: non-linear Dirichlet problems
zbMATH Keywords: open sets with holes
reviewed by: Marco Codegone
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90022-5
OpenAlex ID: W2049447084
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description: scientific article; zbMATH DE number 4073826