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Publication 00-CNA-17

A global method for relaxation in W1,p and in SBVp

Guy Bouchitté
Département de Mathématiques
Université de Toulon
et du Var-BP 132
La Garde Cedex
France 83957

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA, U.S.A.

Giovanni Leoni
Dipartimento di Scienze e Tecnologie Avanzate
Università del Piemonte Orientale
Alessandria, Italy

and

Luísa Mascarenhas
C.M.A.F.
Universidade de Lisboa
Av. Prof. gama Pinto 2
Lisboa Codex, Portugal 1699

 

ABSTRACT: An integral representation formula for a class of functionals defined on W1,p and in SBVp is obtained without requiring the regularity conditions usually imposed in the literature. The approach is based on the general results of [17] and on a Poincaré-Wirtinger's type inequality introduced by De Giorgi, Carriero and Leaci [34]. Applications to relaxation problems and dimension reduction problems in brittle thin films are presented.


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