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 text pdf 10.1512/iumj.2015.64.5503 10.1512/iumj.2015.64.5503 en Indiana Univ. Math. J. 64 (2015) 697 - 733 state-of-the-art mathematics http://iumj.org/access/