Regularity results for vectorial minimizers of a class of degenerate convex integrals
type: Item
instance of: scholarly article
title: Regularity results for vectorial minimizers of a class of degenerate convex integrals
zbMATH Open document ID: 1411.49021
author: Giovanni Cupini
author: Flavia Giannetti
author: Raffaella Giova
author: Antonia Passarelli Di Napoli
published in: Journal of Differential Equations
publication date: 2018-09-06T00:00:00Z
full work available at URL: http://hdl.handle.net/11585/649631
review text: The authors show the higher differentiability and the higher integrability for the gradient of vectorial minimizers of integral functionals with \((p,q)\)-growth conditions. They assume that the non-homogeneous densities are uniformly convex and have a radial structure, with respect to the gradient variable, only at infinity. The results are obtained under a possibly discontinuous dependence on the spatial variable of the integrand. The main features of the energy densities are the following: \begin{itemize}\item they satisfy the so-called \((p,q)\)-growth conditions, \item they are uniformly convex only for large values of \(|\xi|\), \item the partial map \(x\mapsto f(x,\xi)\) is possibly discontinuous. \end{itemize} The study is motivated by the study of optimal transport problems with congestion effects.
reviewed by: Martin Gugat
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 35J47
zbMATH DE Number: 6933418
zbMATH Keywords: regularity
zbMATH Keywords: asymptotic convexity
zbMATH Keywords: minimizer
zbMATH Keywords: \((p,q)\)-growth
zbMATH Keywords: non-autonomous degenerate convex functionals
zbMATH Keywords: vectorial minimizers
MaRDI profile type: Publication
OpenAlex ID: W2809087248
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DOI: 10.1016/J.JDE.2018.06.010
description: scientific article; zbMATH DE number 6933418