Weighted gradient estimates for higher order elliptic systems with non-smooth coefficients

Abstract

In this paper we prove the regularity estimates on the weighted Lorentz spaces for the higher-order elliptic system of equations with non-smooth coefficients on a Lipschitz domain. As a by product, we obtain the regularity estimate on the Lorentz–Morrey spaces. Our results extend previous results to the larger class of Muckenhoupt weights.