Homogenization of a Locally Periodic Oscillating Boundary

Abstract

AbstractThis paper deals with the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The Neumann condition is prescribed on the oscillating part of the boundary, and the Dirichlet condition on a separate part. It is shown that the homogenization result holds in the sense of weak $$L^2$$ L 2 convergence of the solutions and their flows, under natural hypothesis on the regularity of the domain. The strong $$L^2$$ L 2 convergence of average preserving extensions of the solutions and their flows is also considered.