Proof of Schauder estimates for parabolic initial-boundary value model problems via O. A. Ladyzhenskaya's Fourier multipliers theorem (Q2404998)

The author considers model problem for higher order parabolic operators in the sense of Petrovskii. There are obtained estimates of the Hölder norms of the solutions. The proof is based on O. A. Ladyzhenskaya's theorem on the Fourier multipliers in anisotropic Hölder spaces and on K.K. Golovkin's theorem on equivalent norms in these spaces.