@article {2008, title = {Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics}, journal = {Calc. Var. Partial Differential Equations 31 (2008) 137-145}, number = {SISSA;50/2005/M}, year = {2008}, abstract = {In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.}, doi = {10.1007/s00526-006-0084-3}, url = {http://hdl.handle.net/1963/1723}, author = {Gianni Dal Maso and Adriana Garroni} } @article {2014, title = {Dieletric breakdown: optimal bounds}, journal = {Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001}, number = {SISSA;113/00/M}, year = {2001}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1569}, author = {Adriana Garroni and Vincenzo Nesi and Marcello Ponsiglione} } @article {1999, title = {Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case}, journal = {Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58}, number = {SISSA;160/97/M}, year = {1999}, publisher = {Springer}, abstract = {Starting from experimental evidence, the authors justify a variational model for softening phenomena in fracture of one-dimensional bars where the energy is given by the contribution and interaction of two terms: a typical bulk energy term depending on elastic strain and a discrete part that depends upon the jump discontinuities that occur in fracture. A more formal, rigorous derivation of the model is presented by examining the $\\\\Gamma$-convergence of discrete energy functionals associated to an array of masses and springs. Close attention is paid to the softening and fracture regimes. \\nOnce the continuous model is derived, it is fully analyzed without losing sight of its discrete counterpart. In particular, the associated boundary value problem is studied and a detailed analysis of the stationary points under the presence of a dead load is performed. A final, interesting section on the scale effect on the model is included.}, doi = {10.1007/s002050050135}, url = {http://hdl.handle.net/1963/3371}, author = {Andrea Braides and Gianni Dal Maso and Adriana Garroni} } @article {1998, title = {Special functions with bounded variation and with weakly differentiable traces on the jump set}, journal = {NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243}, number = {SISSA;123/95/M}, year = {1998}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1025}, author = {Luigi Ambrosio and Andrea Braides and Adriana Garroni} } @mastersthesis {1994, title = {Asymptotic Behaviour of Dirichlet Problems in Perforated Domains}, year = {1994}, school = {SISSA}, keywords = {Dirichlet problems}, url = {http://hdl.handle.net/1963/5714}, author = {Adriana Garroni} }