Uniform Regularity Estimates in Parabolic Homogenization

By Jun Geng, Zhongwei Shen. 2013

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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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5c21b465e1970173ae5342904e64767f56af3981