W1,p estimates in homogenization of elliptic systems with measurable coefficients in nonsmooth domains
장윤수 · Seoul National University Open Repository (Seoul National University) · 2015
In this study, we establish uniform W 1,p estimates for weak solutions in homogenization of elliptic systems in divergence-form with measurable coefficients in nonsmooth domains.We consider first an interior regularity and then we study boundary value problems, a Dirichlet problem and a conormal derivative problem.Our main purpose is to find an answer for minimal requirements on the coefficients and the boundary condition of the domains to ensure that Calderón-Zygmund theory holds in a homogenization problem.