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Homogenization in a thin domain with an oscillatory boundary

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2011

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Elsevier
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In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type 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 ϵ.

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