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
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 SASFile in questo prodotto:
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