Summary: The author studies two partial differential equations that are posed on perforated domains. The aim is to provide some a priori estimates that do not depend on the size of the performation. The estimates provide more regularity than the usual energy estimates. The first homogenization problem concerns the Laplace- and the mean-curvature operator with Neumann boundary conditions on the perforations. Uniform Lipschitz-estimates for the solutions are shown. The proof is based on the analysis of finite differences that go together with the performation. The result on the mean-curvature operator is used in the analysis of a free boundary system of fluid mechanics. An iteration is studied that involves in one step the inverse of the mean-curvature operator. It is shown that the iteration is contractive. This yields the existence of solutions and uniform estimates. The key point is the use of function spaces that are different from the usual \(L^p\)-spaces.