Schauder estimates for solutions of higher-order parabolic systems
Serena Boccia · Methods and Applications of Analysis · 2013
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 Hölder 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.