On Fourier multipliers in function spaces with partial H\"{o}lder condition and their application to the linearized Cahn-Hilliard equation with dynamic boundary conditions

Abstract

We give relatively simple sufficient conditions on a Fourier multiplier, so that it maps functions with the H$\ddot{o}$lder property with respect to a part of the variables to functions with the H$o$lder property with respect to all variables. With the using of these sufficient conditions we prove the solvability in H$\ddot{o}$lder classes of the initial-boundary value problems for the linearized Cahn-Hilliard equation with dynamic boundary conditions of two types. For the solutions of these problems Schauder estimates are obtained. The final expanded version of this paper is available at AIMS Journals, Evolution Equations and Control Theory (EECT) at http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11870