Journal
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume 108, Issue 6, Pages 952-990Publisher
ELSEVIER
DOI: 10.1016/j.matpur.2017.05.018
Keywords
Free discontinuity problems; Special function of bounded variation; Lower semicontinuity; Relaxation
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Funding
- Italian Ministry of Education, University and Research under the Project Calculus of Variations (PRIN)
- European Research Council [290888]
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We study the lower semicontinuity in GSBV(P)(Omega; R-m) of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending only on the jump set S-u, and of a boundary term, depending on the trace of u on partial derivative Omega 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 can still be represented as the sum of two integrals on S-u and partial derivative Omega, respectively. (C) 2017 Elsevier Masson SAS. All rights reserved.
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