Another look at elliptic homogenization
dc.contributor.area | mathematics | en_US |
dc.contributor.author | Braides, Andrea | |
dc.contributor.author | Cosma Brusca, Giuseppe | |
dc.contributor.author | Donati, Davide | |
dc.date.accessioned | 2023-06-21T09:25:06Z | |
dc.date.available | 2023-06-21T09:25:06Z | |
dc.date.issued | 2023-06-21 | |
dc.description.abstract | We consider the limit of sequences of normalized (s, 2)-Gagliardo seminorms with an oscillating coefficient as s → 1. In a seminal paper by Bourgain, Brezis and Mironescu (subsequently extended by Ponce) it is proven that if the coefficient is constant then this sequence Γ-converges to a multiple of the Dirichlet integral. Here we prove that, if we denote by ε the scale of the oscillations and we assume that 1−s << ε2, this sequence converges to the homogenized functional formally obtained by separating the effects of s and ε; that is, by the homogenization as ε → 0 of the Dirichlet integral with oscillating coefficient obtained by formally letting s → 1 first. | en_US |
dc.identifier.uri | http://hdl.handle.net/1963/35460 | |
dc.language.iso | en_US | en_US |
dc.relation.ispartofseries | 08/2023/MATE; | |
dc.subject | Γ-convergence | en_US |
dc.subject | non-local functionals | en_US |
dc.subject | fractional Sobolev spaces | en_US |
dc.subject | homogenization | en_US |
dc.title | Another look at elliptic homogenization | en_US |
dc.type | Preprint | en_US |
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