Another look at elliptic homogenization

dc.contributor.areamathematicsen_US
dc.contributor.authorBraides, Andrea
dc.contributor.authorCosma Brusca, Giuseppe
dc.contributor.authorDonati, Davide
dc.date.accessioned2023-06-21T09:25:06Z
dc.date.available2023-06-21T09:25:06Z
dc.date.issued2023-06-21
dc.description.abstractWe 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.urihttp://hdl.handle.net/1963/35460
dc.language.isoen_USen_US
dc.relation.ispartofseries08/2023/MATE;
dc.subjectΓ-convergenceen_US
dc.subjectnon-local functionalsen_US
dc.subjectfractional Sobolev spacesen_US
dc.subjecthomogenizationen_US
dc.titleAnother look at elliptic homogenizationen_US
dc.typePreprinten_US
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