Transmission conditions obtained by homogenisation. (December 2018)

• Record Type: Journal Article
• Authors: Dal Maso, Gianni; Franzina, Giovanni; Zucco, Davide
• Is Part Of: Nonlinear analysis. Volume 177(2018)Part A
• Page Start: 361
• Page End: 386
• Publication Date: 2018-12
• Subjects: Γ-convergence -- Capacitary measures -- Neumann sieve; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.04.015
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Given a bounded open set in R n, n ≥ 2, and a sequence ( K j ) 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 ∖ K j, with Neumann boundary conditions on ∂ ( Ω ∖ K j ) . 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 ( K j ) is expressed by means of suitable local minimum problems.