Schauder estimates for solutions of higher-order parabolic systems

Abstract

We prove global Schauder estimates for the derivatives of solutions to non-divergence form higher-order parabolic systems. All coefficients are taken only measurable in the time variable and Hlder continuous in the space variables. Moreover we require that the principal coefficients satisfy the so-called Legendre-Hadamard ellipticity condition. Using such estimates and some classical results, we also give a proof of existence and uniqueness for the Cauchy problem.