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

Now showing 1 - 1 of 1