Local regularity results for minima of functionals of the calculus of variation
type: Item
instance of: scholarly article
title: Local regularity results for minima of functionals of the calculus of variation
zbMATH Open document ID: 0942.49029
DOI: 10.1016/S0362-546X(98)00215-6
author: D. Giachetti
author: Maria Michaela Porzio
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-08-21T00:00:00Z
review text: The authors consider local minima \(v\in W^1_{p,\text{loc}}(\Omega)\) of the variational integral \[ I(v)= \int_\Omega f(x,v,\nabla v) dx \] where \(\Omega\subset\mathbb{R}^n\) is open and \(f\) denotes a Carathéodory function satisfying the growth condition \[ a|\xi|^p\leq f(x,u,\xi)\leq b|\xi|^p+ \varphi_0(x), \] where \(p>1\) and \(\varphi_0\in L^r_{\text{loc}}(\Omega)\) for some \(r>1\). A typical result is the following one: Suppose \(1<p<n\) and \(1< r<{n\over p}\). Then \(v\) is in the space \(L^s_{\text{loc}}(\Omega)\) for \(s\) defined through \({1\over s}={1\over p\cdot r}-{1\over n}\).
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1389521
zbMATH Keywords: minima of functionals
zbMATH Keywords: nonlinear elliptic equations
zbMATH Keywords: regularity of solutions
zbMATH Keywords: variational integral
reviewed by: M. Fuchs
MaRDI profile type: Publication
Wikidata QID: Q126780669
full work available at URL: s0362-546x(98)00215-6
OpenAlex ID: W2034035426
description: scientific article; zbMATH DE number 1389521