Two†parameter anisotropic homogenization for a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. A functional analytic approach

Massimo Lanza de Cristoforis and Paolo Musolino

Mathematische Nachrichten, 2018, vol. 291, issue 8-9, 1310-1341

Abstract: We consider a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δ, and the level of anisotropy of the cell is determined by a diagonal matrix γ with positive diagonal entries. The relative size of each periodic perforation is instead determined by a positive parameter ε. For a given value γ∼ of γ, we analyze the behavior of the unique solution of the problem as (ε,δ,γ) tends to (0,0,γ∼) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.

Date: 2018
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