Boundary estimates for elliptic operators in divergence form with VMO coefficients

Abstract: We establish boundary regularity estimates for elliptic systems in divergence form with VMO coefficients. Additionally, we obtain nondegeneracy estimates of the Hopf-Oleinik type lemma for elliptic equations. In both cases, the moduli of continuity are expressed in terms of the $L^p$-mean oscillations of the coefficients and data.