A lower semicontinuity result for a free-discontinuity functional with a boundary term
Prof. Rodica Toader, Università di Udine
Sala conferenze IMATI-CNR, Pavia - Tuesday, June 6, 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.
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602