Thin domains with doubly oscillatory boundary

摘要

We consider a two-dimensional thin domainwith order of thickness ? that presents oscillations of amplitude also ? 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 ? → 0. We are interested in understanding how this different oscillatory behavior at the boundary, influences the limit problem.