Homogenization of a Locally Periodic Oscillating Boundary

Journal article, 2022

This 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 L2 convergence of the solutions and their flows, under natural hypothesis on the regularity of the domain. The strong L2 convergence of average preserving extensions of the solutions and their flows is also considered.