Gradient estimates for higher order elliptic equations on nonsmooth domains

We establish optimal gradient estimates in Orlicz space for a nonhomogeneous elliptic equation of higher order with discontinuous coefficients on a nonsmooth domain. Our assumption is that for each point and for each sufficiently small scale the coefficients have small mean oscillation and the boundary of the domain is sufficiently close to a hyperplane. As a consequence we prove the classical Wm,p, m=1,2,…, 1<p<∞, estimates for such a higher order equation. Our results easily extend to higher order elliptic and parabolic systems.