Uniform Regularity Estimates in Parabolic Homogenization

Jun Geng; Zhongwei Shen

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arXiv · 1308.5726

Uniform Regularity Estimates in Parabolic Homogenization

Jun Geng·Zhongwei Shen

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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 $W^{1,p}$, Hölder, and Lipschitz estimates as well as boundary $W^{1,p}$ and Hölder estimates, using compactness methods. As a consequence, we establish uniform $W^{1,p}$ estimates for the initial-Dirichlet problems in $C^{1}$ cylinders.

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Jun Geng, Zhongwei Shen. 2013-08-27. Uniform Regularity Estimates in Parabolic Homogenization. https://arxiv.org/abs/1308.5726

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