On second order elliptic equations and variational inequalities with anisotropic principal operators
type: Item
instance of: scholarly article
title: On second order elliptic equations and variational inequalities with anisotropic principal operators
zbMATH Open document ID: 1376.35050
DOI: 10.12775/TMNA.2014.035
author: Vy Khoi Le
published in: Topological Methods in Nonlinear Analysis
publication date: 2017-04-04T00:00:00Z
review text: The following boundary value problem is under consideration: \[ \mathrm{div}[\nabla\Phi(\nabla u)] = f(x, u), \quad u|_{\partial \Omega} = 0, \] where \(\Omega\) is a bounded domain in \({\mathbb R}^{n}\) with sufficiently smooth boundary, the convex function \(\Phi(x): {\mathbb R}^{n}\to [0,\infty]\) satisfies the following conditions: \(\Phi(0)=0\), \(\lim_{x\to \infty} \Phi(x)=\infty\), \(\Phi(x)=\Phi(-x)\) for all \(x\), the set \(\{x:\Phi(x)=\infty\}\) is separated from 0, and \(\Phi\) is lower semicontinuous. The problem is studied in an anisotropic Orlicz-Sobolev space associated with \(\Phi\). Under some additional conditions on the functions \(\Phi,f\), existence of solutions to this problem is proven and the corresponding variational inequality is studied.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J40
zbMATH DE Number: 6700606
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: Dirichlet problem
reviewed by: S. G. Pyatkov
MaRDI profile type: Publication
full work available at URL: tmna.2014.035
OpenAlex ID: W2338123808
description: scientific article; zbMATH DE number 6700606