Boundedness of minimizers of degenerate functionals
type: Item
instance of: scholarly article
title: Boundedness of minimizers of degenerate functionals
zbMATH Open document ID: 0858.49006
published in: Differential and Integral Equations
publication date: 1996-03-17T00:00:00Z
review text: The author considers the functional \(F(u)=\int_\Omega f(x,u,\nabla u)dx\), where \(\Omega\subset\mathbb{R}^n\) \((n\geq2)\) is an open set with finite measure, \(u:\Omega\to\mathbb{R}\), while \(f(x,u,\xi)\) is a real-valued function satisfying the following growth conditions: \(f(x,u,\xi)\geq a(x)H(|u|)|\xi|^p\) and \(f(x,u,0)\leq b(x)B(|u|)\) for a.e. \(x\in\Omega\), \(\forall u\in \mathbb{R}\), \(\forall\xi\in\mathbb{R}^n\), with \(p\geq 1\), \(a\), \(b\) nonnegative measurable functions, \(H\), \(B\) increasing functions in \([0,\infty)\) and \(H(0)>0\). Several conditions on \(a\), \(b\), \(H\), \(B\) are given which assure that a global minimizer of \(F\) on \(W^{1,p}_0(a)\) is bounded.
Mathematics Subject Classification ID: 49J30
Mathematics Subject Classification ID: 49J27
zbMATH DE Number: 856936
zbMATH Keywords: boundedness
zbMATH Keywords: degenerate functionals
zbMATH Keywords: global minimizer
author: A. Mercaldo
reviewed by: Constantin Zălinescu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 856936