Choquet integrals in potential theory
type: Item
instance of: scholarly article
title: Choquet integrals in potential theory
zbMATH Open document ID: 0923.31006
DOI: 10.5565/PUBLMAT_42198_01
author: David R. Adams
published in: Publicacions Matemàtiques
publication date: 1999-10-10T00:00:00Z
full work available at URL: https://eudml.org/doc/41337
review text: This article is a survey about the applications of the Choquet integral to questions in potential theory. The topics include the notion of the Choquet integral as the integral of a function with respect to capacity. A study of the Choquet space \(L^q(C)\) for various choices of the capacity \(C\) is included. The special role of the Hausdorff capacity is given a thorough presentation and the dual spaces and the embeddings of the spaces into more familiar ones is discussed for the case of the Bessel capacity. The author also discusses a general stability criterion for solutions to an obstacle problem for the \(p\)-Laplace operator on a given bounded domain of the \(n\)-space using Choquet integral techniques. Finally the use of the Choquet integral in refining the usual pointwise differentiation theory for functions is discussed. The importance of the article is twofold. Firstly, a large amount of material is reorganized in a most readable form, and secondly, as also emphasized by the author, many of the results discussed in the survey are quite recent so that the presentation makes them better available to the mathematical community.
Mathematics Subject Classification ID: 31C15
Mathematics Subject Classification ID: 28A25
zbMATH DE Number: 1247841
zbMATH Keywords: Choquet integral
zbMATH Keywords: Choquet space
zbMATH Keywords: Hausdorff capacity
zbMATH Keywords: Bessel capacity
zbMATH Keywords: obstacle problem for the \(p\)-Laplace operator
zbMATH Keywords: differentiation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1247841