Unfolding Operator Method for thin domains with a locally periodic highly oscillatory boundary.

Abstract

Analizamos el comportamiento de las soluciones de la ecuación de Poisson con condiciones de Neumann homogéneas en dominios finos bidimensionales que presentan una frontera localmente periódica.

We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media.