@article {dal2017lower, title = {Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation}, journal = {Advances in Calculus of Variations}, volume = {10}, number = {2}, year = {2017}, pages = {183{\textendash}207}, publisher = {De Gruyter}, abstract = {

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.

}, doi = {10.1515/acv-2015-0036}, author = {Gianni Dal Maso and Gianluca Orlando and Rodica Toader} } @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 = {

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.

}, 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} } @article {2014, title = {Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length}, number = {Nonlinear Differential Equations and Applications}, year = {2014}, publisher = {SISSA}, abstract = {

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.

}, keywords = {cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions}, doi = {10.1007/s00030-014-0291-0}, url = {http://hdl.handle.net/1963/7271}, author = {Gianni Dal Maso and Gianluca Orlando and Rodica Toader} } @article {1994, title = {Limits of Dirichlet problems in perforated domains: a new formulation}, journal = {Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360}, number = {SISSA;167/1994/M}, year = {1994}, publisher = {Universit{\`a} degli Studi di Trieste, Dipartimento di Scienze Matematiche}, url = {http://hdl.handle.net/1963/3649}, author = {Gianni Dal Maso and Rodica Toader} }