TY - RPRT
T1 - Gamma-Convergence of Free-discontinuity problems
Y1 - 2017
A1 - Filippo Cagnetti
A1 - Gianni Dal Maso
A1 - Lucia Scardia
A1 - Caterina Ida Zeppieri
AB - We study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper.
PB - SISSA
UR - http://preprints.sissa.it/handle/1963/35276
U1 - 35583
U2 - Mathematics
U4 - 1
ER -