Abstract
We study the Γ-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 Γ-convergence, representation of the Γ-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.
Original language | English |
---|---|
Journal | Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire |
Early online date | 15 Nov 2018 |
DOIs | |
Publication status | E-pub ahead of print - 15 Nov 2018 |
Keywords
- Free-discontinuity problems
- Homogenisation
- Γ-convergence
ASJC Scopus subject areas
- Analysis
- Mathematical Physics
- Applied Mathematics
Fingerprint
Dive into the research topics of 'Γ-convergence of free-discontinuity problems'. Together they form a unique fingerprint.Profiles
-
Lucia Scardia
- School of Mathematical & Computer Sciences - Associate Professor
- School of Mathematical & Computer Sciences, Mathematics - Associate Professor
Person: Academic (Research & Teaching)