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EnglishWe study the lower semicontinuity in $GSBV^{p}(\Om;\R^{m})$ 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~$\partial\Om$. We give sufficient conditions on the integrands for the lower semicontinuity of~$\F$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of~$\F$ can be represented by the sum of two integrals on~$S_{u}$ and~$\partial\Om$, respectively.
A lower semicontinuity result for a free discontinuity functional with a boundary term / Almi, S; Dal Maso, G; Toader, R. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 108:6(2017), pp. 952-990.
| Titolo: | A lower semicontinuity result for a free discontinuity functional with a boundary term |
| Autori: | Almi, S; Dal Maso, G; Toader, R |
| Rivista: | |
| Data di pubblicazione: | 2017 |
| Volume: | 108 |
| Fascicolo: | 6 |
| Pagina iniziale: | 952 |
| Pagina finale: | 990 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.matpur.2017.05.018 |
| URL: | https://doi.org/10.1016/j.matpur.2017.05.018 http://preprints.sissa.it/xmlui/handle/1963/35146 |
| Appare nelle tipologie: | 1.1 Journal article |
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| Alm-DM-Toa-JMPA-2017.pdf | Versione Editoriale (PDF) | Non specificato | Administrator Richiedi una copia |
http://hdl.handle.net/20.500.11767/15979
