01104nas a2200145   4500008004100000245009100041210006900132300001200201490000800213520063400221100001800855700002100873700001900894856004500913       2017                        en  d00aA lower semicontinuity result for a free discontinuity functional with a boundary term0 alower semicontinuity result for a free discontinuity functional   a952-9900 v1083 a<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>1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica  uhttp://hdl.handle.net/20.500.11767/15979