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.

Contact details are reproduced from the original publication and may be historical.

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

A. C. Barroso, J. Matias. “An Ill Posed Problem in SBV_(0)^(2)(Ω).” Journal of Convex Analysis 17 (2010), No. 2, 357–380.