Uniform regularity estimates in parabolic homogenization
Jun GengZhongwei Shen
35K50HomogenizationUniform Regularity Estimates
We consider a family of second-order parabolic systems in divergence form with rapidly oscillating and time-dependent periodic 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.
Indiana University Mathematics Journal
2015
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10.1512/iumj.2015.64.5503
10.1512/iumj.2015.64.5503
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Indiana Univ. Math. J. 64 (2015) 697 - 733
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