Two-parameter homogenization for a nonlinear periodic Robin problem for the Poisson equation: a functional analytic approach

Massimo Lanza de Cristoforis, Paolo Musolino

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Abstract

We consider a nonlinear Robin 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 δδ . The relative size of each periodic perforation is instead determined by a positive parameter ϵϵ . We prove the existence of a family of solutions which depends on ϵϵ and δδ and we analyze the behavior of such a family as (ϵ,δ)(ϵ,δ) tends to (0, 0) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.
Original languageEnglish
Pages (from-to)63-110
JournalRevista Matemática Complutense
Volume31
Issue number1
Early online date09 Sept 2017
DOIs
Publication statusPublished - 01 Jan 2018

Keywords

  • nonlinear robin problem
  • singularly perturbed domain
  • poisson equation
  • periodically perforated domain
  • homogenization
  • real analytic continuation in Banach space

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