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Gamma-Convergence of Free-discontinuity problems

Show simple item record Cagnetti, Filippo Dal Maso, Gianni Scardia, Lucia Zeppieri, Caterina Ida 2017-03-20T13:21:23Z 2017-03-20T13:21:23Z 2017-03-20
dc.description.abstract 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. en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries SISSA;18/2017/MATE
dc.rights the authors en_US
dc.title Gamma-Convergence of Free-discontinuity problems en_US
dc.type Preprint en_US
dc.subject.keyword Free-discontinuity problems
dc.subject.keyword Gamma-convergence
dc.subject.keyword homogenisation
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.relation.firstpage 1 en_US
dc.relation.lastpage 35 en_US

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