TY - JOUR T1 - Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics JF - Calc. Var. Partial Differential Equations 31 (2008) 137-145 Y1 - 2008 A1 - Gianni Dal Maso A1 - Adriana Garroni AB - 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. UR - http://hdl.handle.net/1963/1723 U1 - 2428 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dieletric breakdown: optimal bounds JF - Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 Y1 - 2001 A1 - Adriana Garroni A1 - Vincenzo Nesi A1 - Marcello Ponsiglione PB - SISSA Library UR - http://hdl.handle.net/1963/1569 U1 - 2549 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case JF - Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 Y1 - 1999 A1 - Andrea Braides A1 - Gianni Dal Maso A1 - Adriana Garroni AB - 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. PB - Springer UR - http://hdl.handle.net/1963/3371 U1 - 959 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Special functions with bounded variation and with weakly differentiable traces on the jump set JF - NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243 Y1 - 1998 A1 - Luigi Ambrosio A1 - Andrea Braides A1 - Adriana Garroni PB - SISSA Library UR - http://hdl.handle.net/1963/1025 U1 - 2831 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Asymptotic Behaviour of Dirichlet Problems in Perforated Domains Y1 - 1994 A1 - Adriana Garroni KW - Dirichlet problems PB - SISSA UR - http://hdl.handle.net/1963/5714 U1 - 5566 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER -