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Two‐parameter anisotropic homogenization for a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. A functional analytic approach
Author(s) -
Lanza de Cristoforis Massimo,
Musolino Paolo
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600414
Subject(s) - mathematics , homogenization (climate) , mathematical analysis , diagonal , poisson's equation , anisotropy , dirichlet distribution , poisson distribution , diagonal matrix , dirichlet problem , main diagonal , domain (mathematical analysis) , boundary value problem , geometry , statistics , physics , biodiversity , ecology , quantum mechanics , biology
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.