Abstract. Faremo una breve introduzione al problema di Plateau non parametrico e all'analisi del correlato funzionale area. In codimensione maggiore di 1 vedremo anche il problema stesso di determinare il dominio del funzionale area rilassato è aperto. Alcuni risultati in questa direzione sono stati ottenuti recentemente per mappe definite su domini di R^2 a valori in R^2. Discuteremo talcuni...
Abstract. We prove the rst regularity theorem for the free boundary of solutions to shape optimization problems with integral functionals, for which the energy of a domain is obtained as the integral of a cost function j(u; x) depending on the solution u of a certain PDE problem on Omega. The main feature of these functionals is that (in general) the minimality of a domain cannot be...
Abstract. We consider a family of vectorial models for cohesive fracture, which may incorporate SO(n)-invariance. The deformation belongs to the space of generalized functions of bounded variation and the energy contains an (elastic) volume energy, an opening-dependent jump energy concentrated on the fractured surface, and a Cantor part representing diffuse damage.
In recent a work,...
