Proof of Schauder Estimates for Parabolic Initial-Boundary Value Model Problems VIA O. A. Ladyzhenskaya’s Fourier Multipliers Theorem

Abstract

The paper is concerned with estimates of the Hölder norms of solutions of model parabolic initialboundary value problems in a half-space. 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.