# Boundary Layer Correctors for the Solution of Laplace Equation in a Domain with Oscillating Boundary

### Y. Amirat

Université Blaise Pascal, Aubière, France### O. Bodart

Université Blaise Pascal, Aubière Cedex, France

## Abstract

We study the asymptotic behaviour of the solution of Laplace equation in a domain with very rapidly oscillating boundary. The motivation comes from the study of a longitudinal flow in an infinite horizontal domain bounded at the bottom by a plane wall and at the top by a rugose wall. The rugose wall is a plane covered with periodic asperities which size depends on a small parameter $\epsilon > 0$. The assumption of sharp asperities is made, that is the height of the asperities does not vanish as $\epsilon \to 0$. We prove that, up to an exponentially decreasing error, the solution of Laplace equation can be approximated, outside a layer of width 2$\epsilon$, by a non-oscillating explicit function.

## Cite this article

Y. Amirat, O. Bodart, Boundary Layer Correctors for the Solution of Laplace Equation in a Domain with Oscillating Boundary. Z. Anal. Anwend. 20 (2001), no. 4, pp. 929–940

DOI 10.4171/ZAA/1052