Uniform Estimates in Two Periodic Homogenization Problems
نویسنده
چکیده
We analyze two partial diierential 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 rst homogeniza-tion 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 uid mechanics. A contractive iteration yields the existence of solutions and uniform estimates. The key is the use of function spaces that are diierent from the usual L p-spaces.
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