Thin domains with non-smooth periodic oscillatory boundaries

Abstract

En este trabajo se estudia en detalle como adaptar el método del "operador unfolding" a dominios finos con fronteras que oscilan de forma periódica. El método presentado nos permite analizar las soluciones de la ecuación de Poisson en dominios finos dos dimensionales con fronteras poco regulares.

In this work we study in detail how to adapt the unfolding operator method to thin domains with periodic oscillatory boundaries. We present the unfolding method as a general approach which allows us to analyze the behavior of the solutions of a Neumann problem for equation −Δu+u = f posed in two-dimensional thin domains with an oscillatory boundary. Assuming very mild hypothesis on the regularity of the oscillatory boundary we obtain the homogenized limit problem and corrector results for the three different cases depending on the order of the period of the oscillations.