Uniform estimates in two periodic homogenization problems

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 L"p-spaces. (orig.)SIGLEAvailable from TIB Hannover: RR 1606(99-39) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman