@article {2015,
	title = {A lower semicontinuity result for a free discontinuity functional with a boundary term},
	journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
	volume = {108},
	year = {2017},
	pages = {952-990},
	chapter = {952},
	abstract = {<p>We study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ 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 $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.</p>},
	doi = {10.1016/j.matpur.2017.05.018},
	url = {http://hdl.handle.net/20.500.11767/15979},
	author = {Stefano Almi and Gianni Dal Maso and Rodica Toader}
}
