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Relaxation in BV for a class of functionals without continuity assumptions. (English) Zbl 1153.49016

Summary: This paper is devoted to prove new relaxation and \(\Gamma\)-convergence theorems on \(\text{BV}(\Omega)\) for a class of integral functionals, whose integrands have a product type structure, but they do not satisfy any assumptions of coerciveness or continuity with respect to the spatial variable.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
49Q20 Variational problems in a geometric measure-theoretic setting
49M20 Numerical methods of relaxation type
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