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Communicated by: W. Wendland MSC Classification: 35J57; 74E30; 35B65 35D30We study global gradient estimates for the weak solution to elliptic systems with measurable coefficients from composite materials in a nonsmooth bounded domain. The principal coefficients are assumed to be merely measurable in one variable and have small bounded mean oscillation (BMO) seminorms in the other variables on each subdomain whose boundary satisfies the so-called δ-Reifenberg flat condition. Under these assumptions and based on our new geometric observation for disjoint Reifenberg domains in a previous study, we obtain global W 1,p estimates.

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<abstract><p>We obtain an approximation result of the weak solutions to elliptic and parabolic equations with Dirichlet boundary conditions. We show that the weak solution can be obtained with a limit of approximations by regularizing the nonlinearities and approximating the domains.</p></abstract>