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Journal of Convex Analysis 17 (2010), No. 2, 357--380
Copyright Heldermann Verlag 2010

An Ill Posed Problem in SBV02(Ω)

Ana Cristina Barroso
CMAF, Universidade de Lisboa, Av. Prof. Gama, Pinto 2, 1649-003 Lisboa, Portugal
and: Dep. de Matemática, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal

José Matias
Dep. de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal

We study existence of solutions in SBV02(Ω) of a variational problem involving bulk and interfacial energy terms, but with the bulk energy not attaining a minimum at the prescribed boundary value. We obtain an expression for the relaxed energy and give some properties satisfied by the solutions of the relaxed problem.

Keywords: Functions of bounded variation, relaxation.

MSC: 49J45, 49K24, 35E99

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