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

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

Keywords

  • Functions of bounded variation
  • relaxation

Mathematics Subject Classification

49J45, 49K24, 35E99

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

Download BibTeXPublished by Heldermann Verlag.

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