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, Paolo Musolino

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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 math formula of γ, we analyze the behavior of the unique solution of the problem as math formula tends to math formula by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.
Original languageEnglish
Pages (from-to)1310-1341
Number of pages32
JournalMathematische Nachrichten
Volume291
Issue number8-9
Early online date25 Jan 2018
DOIs
Publication statusPublished - 01 Jun 2018

Keywords

  • anisotropic homogenization
  • Dirichlet problem
  • integral equations
  • Poisson equation
  • periodically perforated domain
  • real analytic continuation in Banach space
  • singularly perturbed domain

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