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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Published in | Journal of the European Mathematical Society : JEMS Vol. 23; no. 3; pp. 701 - 719 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
European Mathematical Society
01.01.2021
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 1435-9855 1435-9863 |
DOI: | 10.4171/jems/1021 |