Thin domains with doubly oscillatory boundary

We consider a 2-dimensional thin domain with order of thickness ε which presents oscillations of amplitude also ε 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 as the parameter ε goes to 0. We are interested in understanding how this different oscillatory behavior at the boundary, influences the limit problem.

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