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periodically perforated domain

Proceedings of the Edinburgh Mathematical Society (1)

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Asymptotic Behaviour of the Energy Integral of a Two-Parameter Homogenization Problem with Nonlinear Periodic Robin Boundary Conditions
Part of
Massimo Lanza de Cristoforis, Paolo Musolino
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 4 / November 2019

Published online by Cambridge University Press:

22 March 2019, pp. 985-1016
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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 δ. The relative size of each periodic perforation is determined by a positive parameter ε. Under suitable assumptions, such a problem admits a family of solutions which depends on ε and δ. We analyse the behaviour the energy integral of such a family as (ε, δ) tends to (0, 0) by an approach that represents an alternative to asymptotic expansions and classical homogenization theory.