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A Relaxation result for energies defined on pairs set-function and applications

Braides, Andrea and Chambolle, Antonin and Solci, Margherita (2007) A Relaxation result for energies defined on pairs set-function and applications. ESAIM. Control, Optimisation and Calculus of Variations, Vol. 13 (4), p. 717-734. eISSN 1262-3377. Article.

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DOI: 10.1051/cocv:2007032

Abstract

We consider, in an open subset Ω of RN, energies depending on the perimeter of a subset E С Ω (or some equivalent surface integral) and on a function u which is defined only on E. We compute the lower semicontinuous envelope of such energies. This relaxation has to take into account the fact that in the limit, the “holes” Ω \ E may collapse into a discontinuity of u, whose surface will be counted twice in the relaxed energy. We discuss some situations where such energies appear, and give, as an application, a new proof of convergence for an extension of Ambrosio-Tortorelli’s approximation to the Mumford-Shah functional.

Item Type:Article
ID Code:812
Status:Published
Refereed:Yes
Uncontrolled Keywords:Relaxation, free discontinuity problems, Γ-convergence
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Divisions:001 Università di Sassari > 01 Dipartimenti > Architettura e pianificazione
Publisher:EDP Sciences, SMAI
eISSN:1262-3377
Publisher Policy:Depositato in conformità con la politica di copyright dell'Editore
Deposited On:18 Aug 2009 10:03

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