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

¹ 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.
² Mathématiques, Université d'Orléans, rue de Chartres, 45067 Orléans Cedex 2, France; prignet@labomath.univ-orleans.fr.

Received: 27 June 2002
Revised: 17 January 2003

Abstract

We study the sequence u_n, which is solution of in Ω an open bounded set of R^N and u_n= 0 on ∂Ω, when f_n 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.