Compactness and lower semicontinuity in $GSBD

In this paper we prove a compactness and semicontinuity result in GSBD for sequences with bounded Griffith energy. This generalises classical results in ( G ) SBV by Ambrosio [1, 2, 4] and SBD by Bellettini–Coscia–Dal Maso [9]. As a result, the static problem in Francfort–Marigo’s variational approa...

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Bibliographic Details
Published inJournal of the European Mathematical Society : JEMS Vol. 23; no. 3; pp. 701 - 719
Main Authors Chambolle, Antonin, Crismale, Vito
Format Journal Article
LanguageEnglish
Published European Mathematical Society 01.01.2021
Subjects
Functional Analysis
Mathematics
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Summary:In this paper we prove a compactness and semicontinuity result in GSBD for sequences with bounded Griffith energy. This generalises classical results in ( G ) SBV by Ambrosio [1, 2, 4] and SBD by Bellettini–Coscia–Dal Maso [9]. As a result, the static problem in Francfort–Marigo’s variational approach to crack growth [30] admits (weak) solutions.
ISSN:1435-9855
1435-9863
DOI:10.4171/jems/1021