Abstract
We analyze two partial differential equations that are posed on perforated domains. We provide a priori estimates that do not depend on the size of the perforation: A sequence of solutions is uniformly bounded in a Sobolev space of regular functions. The first homogenization problem concerns the Laplace and the mean-curvature operator with Neumann boundary conditions. We derive uniform Lipschitz estimates for the solutions. The result is used in the analysis of a free boundary system of fluid mechanics. A contractive iteration yields the existence of solutions and uniform estimates. The key is the use of function spaces that are different from the usual Lp-spaces. © 2000 John Wiley & Sons, Inc.
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