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G-Convergence of free discontinuity problems
journal contribution
posted on 2023-06-09, 15:57 authored by Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida ZeppieriWe study the G-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 G-convergence, representation of the G-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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Annales de l'Institut Henri Poincaré C, Analyse Non LinéaireISSN
0294-1449Publisher
ElsevierExternal DOI
Issue
4Volume
36Page range
1035-1079Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-11-20First Open Access (FOA) Date
2019-11-15First Compliant Deposit (FCD) Date
2018-11-19Usage metrics
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