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 et al. (Another look at Sobolev spaces. In: Optimal control and partial differential equations. IOS, Amsterdam, pp 439–455, 2001) 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<[removed]
Another Look at Elliptic Homogenization / Braides, A.; Brusca, G. C.; Donati, D.. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - (2024). [10.1007/s00032-023-00389-y]
Another Look at Elliptic Homogenization
Braides A.
;Brusca G. C.;Donati D.
2024-01-01
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 et al. (Another look at Sobolev spaces. In: Optimal control and partial differential equations. IOS, Amsterdam, pp 439–455, 2001) 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<[removed]| File | Dimensione | Formato | |
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