Homogenization of the boundary value problem for the poisson equation with rapidly oscillating nonlinear boundary conditions: space dimension n ≥ 3, critical case

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Abstract

The homogenization of the Poisson equation in a bounded domain with rapidly oscillating boundary conditions specied on a part of the domain boundary is studied. A Neumann boundary condition alternates with an ε-periodically distributed nonlinear Robin condition involving the coefficient ε−β, where β ∈ R. The diameter of the boundary portions with a nonlinear Robin condition is of order O(εα), α > 1. A critical relation between the parameters α and β is considered

About the authors

A. V. Podolskiy

Moscow State University

Email: shaposh.tan@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991

T. A. Shaposhnikova

Moscow State University

Author for correspondence.
Email: shaposh.tan@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991

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