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Uniform Regularity Estimates in Parabolic Homogenization (1308.5726v1)
Published 27 Aug 2013 in math.AP
Abstract: We consider a family of second-order parabolic systems in divergence form with rapidly oscillating and time-dependent coefficients, arising in the theory of homogenization. We obtain uniform interior $W{1,p}$, H\"older, and Lipschitz estimates as well as boundary $W{1,p}$ and H\"older estimates, using compactness methods. As a consequence, we establish uniform $W{1,p}$ estimates for the initial-Dirichlet problems in $C{1}$ cylinders.