Regularization of a set function -- application to integral representation
type: Item
instance of: scholarly article
title: Regularization of a set function -- application to integral representation
zbMATH Open document ID: 1009.49014
author: Michel Bellieud
author: Guy Bouchitté
published in: Ricerche di Matematica
publication date: 2003-03-18T00:00:00Z
review text: In this paper the authors consider a variational functional \({\mathcal F}(u;A)\) assuming that the gauge function is majorized by a given random measure \(\mu\) on \({\mathbb{R}}^n\). In the context of integral representation \(\mu\) is associated with the growth condition. The main result is that for a fixed \(\mu\), the measure \(\lambda:={\mathcal F}(u;\cdot)\) can be recovered from the set function \(S:=m(u;\cdot)\) due to a variant of the Carathéodory construction, where \[ m(u;A)=\inf \{{\mathcal F}(u+\varphi;A):\operatorname{spt}\varphi\subset\subset A\}. \]
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 1884336
zbMATH Keywords: variational functional
zbMATH Keywords: integral representation
reviewed by: Stefan Balint
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1884336