Thin domains with doubly oscillatory boundary

Abstract

Consideramos dominios finos bidimensionales que presentan oscilaciones en la frontera superior e inferior. Estudiamos el comportamiento de las soluciones de la ecuación de Laplace con condiciones de Neumann y obtenemos el problema límite homogeneizado.

We consider a two-dimensional thin domain that presents oscillations on both boundaries, top and bottom, but the period of the oscillations are of different order at the top and at the bottom. We study the behavior of the Laplace operator with Neumann boundary condition and obtain its asymptotic homogenized limit. We are interested in understanding how this different oscillatory behavior at the boundary, influences the limit problem