On regularity for nonhomogeneous parabolic systems with a skew-symmetric part in BMO

Abstract

In this paper we investigate the improved Caccioppoli inequality and the reverse Hölder inequality for gradients of weak solutions to nonhomogeneous parabolic systems whose coefficients can be split into a complex-valued and bounded part, which also satisfies the uniform G$\mathring{a}$rding inequality, and a real and anti-symmetric part in BMO. In particular, unbounded coefficients are allowed.