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A lower semicontinuity result for a free-discontinuity functional with a boundary term
Prof. Rodica Toader, Universitą di Udine
Sala conferenze IMATI-CNR, Pavia - Martedì 6 Giugno 2017 h.15:00
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 surface 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.
The results were obtained together with S. Almi and G. Dal Maso.
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