Regularization of an unilateral obstacle problem
type: Item
instance of: scholarly article
title: Regularization of an unilateral obstacle problem
zbMATH Open document ID: 0991.35038
author: Ahmed Addou
author: Jamal Zahi
author: E. Bekkaye Mermri
publication date: 2002-03-20T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/194082
Mathematics Subject Classification ID: 35J85
zbMATH DE Number: 1721514
zbMATH Keywords: regularization methods
zbMATH Keywords: non-differentiable minimization problem
MaRDI profile type: Publication
OpenAlex ID: W1979757175
cites work: Q4898349
cites work: Q4767831
cites work: Q3914338
cites work: The regularization method for an obstacle problem
cites work: Q3905599
DOI: 10.1051/M2AN:2001144
published in: M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
review text: The authors consider the following unilateral obstacle problem: Find NEWLINE\[NEWLINEu\in K=\bigl\{v \in H^1(\Omega): v\geq\psi \text{ a.e. in }\Omega,\;v=g \text{ on }\partial \Omega\bigr\},NEWLINE\]NEWLINE such that NEWLINE\[NEWLINE\int_\Omega\nabla u\nabla(v-u) dx+\langle f,v-u \rangle\geq 0\quad \text{for all }v\in K,NEWLINE\]NEWLINE where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) with smooth boundary \(\partial\Omega\), \(g\in H^{1/2} (\partial \Omega)\), \(\psi\in H^1(\Omega)\) and \(f\in H^1(\Omega)\). An existence result as well as the uniqueness of the solution of the above problem comes from [\textit{D. Kinderlehrer} and \textit{G. Stampacchia}, An introduction to variational inequalities and their applications, Pure Appl. Math. 88 (1980; Zbl 0457.35001)]. The authors develop a regularization method for solving a non-differentiable minimization problem equivalent to the above one. To this end they approximate the non-differentiable term by a sequence of differentiable ones. The paper is a generalization of [\textit{H. Huang}, \textit{W. Han} and \textit{J. Zhou}, Numer. Math. 69, 155-166 (1994; Zbl 0817.65050)].
reviewed by: Leszek Gasiński
description: scientific article; zbMATH DE number 1721514