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Abstract
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.
Author information
Contact details are reproduced from the original publication and may be historical.
AC
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
JM
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.