Regularity results for minimizers of integral functionals with nonstandard growth in Carnot-Carathéodory spaces
type: Item
instance of: scholarly article
title: Regularity results for minimizers of integral functionals with nonstandard growth in Carnot-Carathéodory spaces
zbMATH Open document ID: 1189.49058
DOI: 10.4171/RLM/566
author: Flavia Giannetti
author: Antonia Passarelli Di Napoli
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2010-05-31T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: We prove regularity results for minimizers of integral functionals of the type \[ \int_\Omega f(Xu)\,dx, \] where \(f\) satisfies a nonstandard growth condition and \(Xu\) stands for the horizontal gradient of \(u\). More precisely, we obtain regularity in the scale of Campanato spaces without assuming any restriction on the growth exponents and, under a suitable assumption on them, we get the local boundedness as well as an higher integrability result for the gradient.
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 49K27
zbMATH DE Number: 5714230
zbMATH Keywords: nonstandard growth conditions
zbMATH Keywords: Carnot-Carathéodory spaces
zbMATH Keywords: regularity
MaRDI profile type: Publication
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OpenAlex ID: W1975497217
description: scientific article; zbMATH DE number 5714230