A lower semicontinuity result for a free discontinuity functional with a boundary term
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Almi, Stefano | |
| dc.contributor.author | Dal Maso, Gianni | |
| dc.contributor.author | Toader, Rodica | |
| dc.date.accessioned | 2015-12-17T08:23:17Z | |
| dc.date.available | 2015-12-17T08:23:17Z | |
| dc.date.issued | 2015-12-15 | |
| dc.description.abstract | We 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. | en_US |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/35146 | |
| dc.language.iso | en | en_US |
| dc.miur.area | 1 | en_US |
| dc.subject | Free discontinuity problems | en_US |
| dc.subject | Special function of bounded variation | en_US |
| dc.subject | Lower semicontinuity | en_US |
| dc.subject | Relaxation | en_US |
| dc.subject.miur | MAT/05 | en_US |
| dc.title | A lower semicontinuity result for a free discontinuity functional with a boundary term | en_US |
| dc.type | Preprint | en_US |