A Global Method for Relaxation in W1,p and in SBVp |
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| Authors: | GUY BOUCHITTÉ IRENE FONSECA GIOVANNI LEONI LUÍSA MASCARENHAS |
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| Affiliation: | (1) Département de Mathématiques, Université de Toulon et du Var-BP 132, La Garde Cedex, France 83957 e-mail: bouchitte@univ-tln.fr, FR;(2) Department of Mathematical Sciences, Carnegie-Mellon University, Pittsburgh, PA, U.S.A. e-mail: fonseca@andrew.cmu.edu giovanni@andrew.cmu.edu, US;(3) C.M.A.F., Universidade de Lisboa, Av. Prof. gama Pinto 2, Lisboa Codex, Portugal 1699 e-mail: mascar@ptmat.cmc.fc.ul.pt, PT |
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| Abstract: | An integral representation formula for a class of functionals defined on and in (the space of special functions of bounded variation) is obtained without requiring the regularity conditions usually imposed in the literature. The approach is based on the general results of [10] and on a Poincaré-Wirtinger type inequality introduced by DE GIORGI, CARRIERO & LEACI [25]. Applications to relaxation problems and dimension-reduction problems in brittle thin films are presented. (Accepted May 8, 2002) Published online October 18, 2002 Communicated by L. Ambrosio |
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