TY - JOUR T1 - Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation JF - Advances in Calculus of Variations Y1 - 2017 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader AB -

We study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

PB - De Gruyter VL - 10 ER - TY - JOUR T1 - A lower semicontinuity result for a free discontinuity functional with a boundary term JF - Journal de Mathématiques Pures et Appliquées Y1 - 2017 A1 - Stefano Almi A1 - Gianni Dal Maso A1 - Rodica Toader AB -

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.

VL - 108 UR - http://hdl.handle.net/20.500.11767/15979 IS - 6 U1 - 34731 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length Y1 - 2014 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader KW - cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions AB -

We consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

PB - SISSA UR - http://hdl.handle.net/1963/7271 U1 - 7316 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Limits of Dirichlet problems in perforated domains: a new formulation JF - Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360 Y1 - 1994 A1 - Gianni Dal Maso A1 - Rodica Toader PB - Università degli Studi di Trieste, Dipartimento di Scienze Matematiche UR - http://hdl.handle.net/1963/3649 U1 - 656 U2 - Mathematics U3 - Functional Analysis and Applications ER -