Abstract
We study the Γconvergence of sequences of freediscontinuity functionals depending on vectorvalued 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 Γconvergence, representation of the Γlimit 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 byproduct of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper.
Original language  English 

Journal  Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 
Early online date  15 Nov 2018 
DOIs  
Publication status  Epub ahead of print  15 Nov 2018 
Keywords
 Freediscontinuity problems
 Homogenisation
 Γconvergence
ASJC Scopus subject areas
 Analysis
 Mathematical Physics
 Applied Mathematics
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Profiles

Lucia Scardia
 School of Mathematical & Computer Sciences  Associate Professor
 School of Mathematical & Computer Sciences, Mathematics  Associate Professor
Person: Academic (Research & Teaching)