We study the lower semicontinuity in GSBVp(Ω;Rm) of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending only on the jump set Su, and of a boundary term, depending on the trace of u on ∂Ω. We give necessary and sufficient conditions on the integrands for the lower semicontinuity of F. Moreover, we prove a relaxation result, which shows that the lower semicontinuous envelope of F can still be represented as the sum of two integrals on Su and ∂Ω, respectively. © 2017 Elsevier Masson SAS
A lower semicontinuity result for a free discontinuity functional with a boundary term / Almi, Stefano; Dal Maso, Gianni; Toader, Rodica. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 108:6(2017), pp. 952-990. [10.1016/j.matpur.2017.05.018]
A lower semicontinuity result for a free discontinuity functional with a boundary term
Toader, Rodica
2017-01-01
Abstract
We study the lower semicontinuity in GSBVp(Ω;Rm) of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending only on the jump set Su, and of a boundary term, depending on the trace of u on ∂Ω. We give necessary and sufficient conditions on the integrands for the lower semicontinuity of F. Moreover, we prove a relaxation result, which shows that the lower semicontinuous envelope of F can still be represented as the sum of two integrals on Su and ∂Ω, respectively. © 2017 Elsevier Masson SASPubblicazioni consigliate
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