Title: Weighted $L_{p,q}$-estimates for higher order elliptic and parabolic systems with BMO coefficients on Reifenberg flat domains,
Abstract: We prove weighted $L_{p,q}$-estimates for divergence type higher order
elliptic and parabolic systems with irregular coefficients on Reifenberg flat
domains. In particular, in the parabolic case the coefficients do not have any
regularity assumptions in the time variable. As functions of the spatial
variables, the leading coefficients are permitted to have small mean
oscillations. The weights are in the class of Muckenhoupt weights $A_p$. We
also prove the solvability in weighted Sobolev spaces for the systems in the
whole space, on a half space, and on bounded Reifenberg flat domains.