Homogenization in a thin domain with an oscillatory boundary

Abstract

In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type $R^{\epsilon }=\{(x,y)\in {\mathbb{R}}^2;x\in (0,1),0<y<\epsilon G(x,x/\epsilon )\}$ where the function G(x,y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter $\epsilon$.

27 pages, 2 figures

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