Existence and uniqueness of solutions for nonlinear obstacle problems with measure data
type: Item
instance of: scholarly article
title: Existence and uniqueness of solutions for nonlinear obstacle problems with measure data
zbMATH Open document ID: 0967.35056
DOI: 10.1016/S0362-546X(99)00190-X
author: Chiara Leone
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-12-19T00:00:00Z
review text: This paper deals with obstacle problems with measure data associated to a nonlinear elliptic differential operator of monotone type, mapping \(W^{1,p}_0(\Omega)\), \(p>1\), into \(W^{-1,p'}(\Omega)\). The author considers as data bounded Radon measures vanishing on sets of capacity zero and introduce a definition of ``entropy'' solution for obstacle problems ``similar'' to the characterization given by Kinderlehrer and Stampacchia for data in \(W^{-1,p'}(\Omega)\). The existence of such a solution is proved by an approximation technique, the uniqueness is implicit in the definition. The found solution is characterized by the complementarity system and a stability result with respect to a strong convergence is proved.
reviewed by: Maria Agostina Vivaldi
Mathematics Subject Classification ID: 35J85
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35R05
zbMATH DE Number: 1545351
zbMATH Keywords: nonlinear obstacle problems
zbMATH Keywords: measure data
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: entropy solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1545351