Given a bounded open set in Rn, n≥2, and a sequence (Kj) of compact sets converging to an (n-1)-dimensional manifold M, we study the asymptotic behaviour of the solutions to some minimum problems for integral functionals on Ω\Kj, with Neumann boundary conditions on ∂(Ω\Kj). We prove that the limit of these solutions is a minimiser of the same functional on Ω\M subjected to a transmission condition on M, which can be expressed through a measure µ supported on M. The class of all measures that can be obtained in this way is characterised, and the link between the measure µ and the sequence (Kj) is expressed by means of suitable local minimum problems.

Transmission conditions obtained by homogenisation / Dal Maso, Gianni; Franzina, Giovanni; Zucco, Davide. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 177, Part A:December(2018), pp. 361-386. [10.1016/j.na.2018.04.015]

Transmission conditions obtained by homogenisation

Dal Maso, Gianni
;
Franzina, Giovanni;Zucco, Davide
2018

Abstract

Given a bounded open set in Rn, n≥2, and a sequence (Kj) of compact sets converging to an (n-1)-dimensional manifold M, we study the asymptotic behaviour of the solutions to some minimum problems for integral functionals on Ω\Kj, with Neumann boundary conditions on ∂(Ω\Kj). We prove that the limit of these solutions is a minimiser of the same functional on Ω\M subjected to a transmission condition on M, which can be expressed through a measure µ supported on M. The class of all measures that can be obtained in this way is characterised, and the link between the measure µ and the sequence (Kj) is expressed by means of suitable local minimum problems.
177, Part A
December
361
386
https://www.sciencedirect.com/science/article/pii/S0362546X18301020?via%3Dihub
Dal Maso, Gianni; Franzina, Giovanni; Zucco, Davide
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/85678
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