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Boundary homogenization in domains with randomly oscillating boundary

Authors:	Youcef Amirat Andrey L Piatnitski

Institution:	^a Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal, 63177 Aubière cedex, France ^b Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991, Russia ^c Narvik University College, Postboks 385, 8505 Narvik, Norway ^d P.N. Lebedev Physical Institute RAS, Leninski pr., 53, Moscow 117924, Russia

Abstract:	We consider a model homogenization problem for the Poisson equation in a domain with a rapidly oscillating boundary which is a small random perturbation of a fixed hypersurface. A Fourier boundary condition with random coefficients is imposed on the oscillating boundary. We derive the effective boundary condition, prove a convergence result, and establish error estimates.

Keywords:	Boundary homogenization Random oscillating boundary Effective boundary condition
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