Periodic unfolding for anisotropically bounded sequences

Article type: Research Article

Authors: Falconi, Riccardo^a | Griso, Georges^{b; *} | Orlik, Julia^a

Affiliations: [a] Fraunhofer ITWM, 67663 Kaiserslautern, Germany | [b] Sorbonne Université, CNRS, Université de Paris, Laboratoire Jacques-Louis Lions (LJLL), F-75005 Paris, France

Correspondence: [*] Corresponding author. E-mail: griso@ljll.math.upmc.fr.

Abstract: This paper is focused on the asymptotic behavior of sequences of functions, whose partial derivatives estimates in one or more directions are highly contrasted with respect to the periodic parameter ε. In particular, a direct application for the homogenization of a homogeneous Dirichlet problem defined on an anisotropic structure is presented. In general, the obtained results can be applied to thin structures where the behavior is different according to the observed direction.

Keywords: Periodic unfolding method, homogenization, anisotropic Sobolev spaces, Dirichlet problem

DOI: 10.3233/ASY-221796

Journal: Asymptotic Analysis, vol. 132, no. 3-4, pp. 383-407, 2023