Integral functionals determined by their minima
type: Item
instance of: scholarly article
title: Integral functionals determined by their minima
zbMATH Open document ID: 0613.49028
author: Luciano Modica
author: G. Dal Maso
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108045
review text: The authors prove that the integrand \(f=f(x,p)\) of an integral functional of the type \[ F(u,A)=\int_{A}f(x,Du(x))dx \] may be found by the knowledge of the minima of the Dirichlet problems for F with linear boundary values. More precisely, they show that f(x,p) may be obtained by a differentiation process of the set function \(A\to m(p,A)\) where A is a bounded open subset of \(R^ n\) which belongs to a particular family and \(m(p,A)=\min \{F(u,A):\) \(u(x)=p\cdot x\), \(x\in \partial A\}\).
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 28A15
zbMATH DE Number: 3992292
zbMATH Keywords: integral functional
zbMATH Keywords: minima
zbMATH Keywords: Dirichlet problems
reviewed by: Rosanna Schianchi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3992292