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

Autor:	Degtyarev, S. P.
Rok vydání:	2014
Předmět:	Mathematics - Analysis of PDEs 42B15 42B37 35G15 35G16 35R35
Druh dokumentu:	Working Paper
Popis:	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 Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1402.7212 Zobrazit plný text záznamu View this record from Arxiv