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Orlicz capacities and applications to some existence questions for elliptic pdes having measure data

Published online by Cambridge University Press:  15 September 2003

Alberto Fiorenza  and
Alain Prignet
Alberto Fiorenza
Affiliation:
Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli, via Monteoliveto 3, 80134 Napoli, Italy, and Istituto per le Applicazioni del Calcolo “Mauro Picone", Sezione di Napoli, Consiglio Nazionale delle Ricerche, via Pietro Castellino 111, 80131 Napoli, Italy; fiorenza@unina.it.
Alain Prignet
Affiliation:
Mathématiques, Université d'Orléans, rue de Chartres, 45067 Orléans Cedex 2, France; prignet@labomath.univ-orleans.fr.
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Abstract

We study the sequence un, which is solution of $-{\rm div}(a(x,{\nabla}u_n)) + \Phi''(|u_n|)\,u_n= f_n+ g_n$ in Ω an open bounded set of RN and un= 0 on ∂Ω, when fn tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N-function Φ, and prove a non-existence result.

Keywords

Elliptic equationOrlicz spacemeasurecapacity.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 317 - 341
Copyright
© EDP Sciences, SMAI, 2003

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