Zhongwei Shen

Convergence Rates in L 2 for Elliptic Homogenization Problems

We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems

On absolute continuity of the periodic Schrödinger operators

{\{\mathcal{L}_\varepsilon\}}

L^{p}

with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of

Homogenization of Stokes Systems and Uniform Regularity Estimates

{\{\mathcal{L}_\varepsilon\}}

Convergence rates in periodic homogenization of systems of elasticity

. Most of our results, which rely on the recently established uniform estimates for the L2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains.

Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

The main purpose of this work is to study uniform regularity estimates for a family of elliptic operators