Abstract

We study existence of solutions in SBV02(Ω)SBV_0^2(\Omega) 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.

Author information

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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

Keywords

  • Functions of bounded variation
  • relaxation

Mathematics Subject Classification

49J45, 49K24, 35E99

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Suggested citation

A. C. Barroso, J. Matias. “An Ill Posed Problem in SBV_0^2(Ω).” Journal of Convex Analysis 17 (2010), No. 2, 357–380. https://doi.org/10.68381/jca17026

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press LLC.