%0 Journal Article %J Calc. Var. Partial Differential Equations 31 (2008) 137-145 %D 2008 %T Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics %A Gianni Dal Maso %A Adriana Garroni %X 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. %B Calc. Var. Partial Differential Equations 31 (2008) 137-145 %G en_US %U http://hdl.handle.net/1963/1723 %1 2428 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-26T12:52:13Z\\nNo. of bitstreams: 1\\nmath.AP0507088.pdf: 132125 bytes, checksum: 444c743b7852d0f6e97bb318f49b4467 (MD5) %R 10.1007/s00526-006-0084-3 %0 Journal Article %J Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 %D 2001 %T Dieletric breakdown: optimal bounds %A Adriana Garroni %A Vincenzo Nesi %A Marcello Ponsiglione %B Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 %I SISSA Library %G en %U http://hdl.handle.net/1963/1569 %1 2549 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:17Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 2000 %0 Journal Article %J Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 %D 1999 %T Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case %A Andrea Braides %A Gianni Dal Maso %A Adriana Garroni %X 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. %B Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 %I Springer %G en_US %U http://hdl.handle.net/1963/3371 %1 959 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-28T17:18:31Z\\nNo. of bitstreams: 1\\nVariational_formulation.pdf: 2100868 bytes, checksum: 88bfc4cfb6072391f1c6d7cd06e7b8ec (MD5) %R 10.1007/s002050050135 %0 Journal Article %J NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243 %D 1998 %T Special functions with bounded variation and with weakly differentiable traces on the jump set %A Luigi Ambrosio %A Andrea Braides %A Adriana Garroni %B NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243 %I SISSA Library %G en %U http://hdl.handle.net/1963/1025 %1 2831 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:50Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Thesis %D 1994 %T Asymptotic Behaviour of Dirichlet Problems in Perforated Domains %A Adriana Garroni %K Dirichlet problems %I SISSA %G en %U http://hdl.handle.net/1963/5714 %1 5566 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-04-16T10:54:30Z\\nNo. of bitstreams: 1\\nPhD_Garroni_Adriana.pdf: 8799112 bytes, checksum: 71df771317b5fd6f6add4ee83805d0e5 (MD5)