Gamma-Convergence of Free-discontinuity problems

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dc.contributor.areaMathematicsen_US
dc.contributor.authorCagnetti, Filippo
dc.contributor.authorDal Maso, Gianni
dc.contributor.authorScardia, Lucia
dc.contributor.authorZeppieri, Caterina Ida
dc.date.accessioned2017-03-20T13:21:23Z
dc.date.available2017-03-20T13:21:23Z
dc.date.issued2017-03-20
dc.description.abstractWe 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.identifier.urihttps://openscience.sissa.it/handle/1963/35276
dc.language.isoenen_US
dc.miur.area1en_US
dc.publisherSISSAen_US
dc.relation.firstpage1en_US
dc.relation.ispartofseriesSISSA;18/2017/MATE
dc.relation.lastpage35en_US
dc.rightsthe authorsen_US
dc.subject.keywordFree-discontinuity problems
dc.subject.keywordGamma-convergence
dc.subject.keywordhomogenisation
dc.titleGamma-Convergence of Free-discontinuity problemsen_US
dc.typePreprinten_US
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