ON FOURIER MULTIPLIERS IN FUNCTION SPACES WITH PARTIAL HOLDER CONDITION AND THEIR APPLICATION TO THE LINEARIZED CAHN-HILLIARD EQUATION WITH DYNAMIC BOUNDARY CONDITIONS

被引：2

作者：

Degtyarev, Sergey P. ^{[1
]}

机构：

[1] State Inst Appl Math & Mech, Inst Appl Math & Mech NASU, R Luxenburg Str 74, UA-83114 Donetsk, Ukraine

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2015年 / 4卷 / 04期

关键词：

Fourier multipliers; Holder spaces; partial regularity; dynamic boundary conditions; Cahn-Hilliard equation; PARABOLIC EQUATIONS; CLASSICAL SOLUTION; STEFAN PROBLEM; ASYMPTOTIC-BEHAVIOR; MUSKAT PROBLEM; REGULARITY; EXISTENCE;

D O I：

10.3934/eect.2015.4.391

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give relatively simple sufficient conditions on a Fourier multiplier so that it maps functions with the Holder property with respect to a part of the variables to functions with the Holder property with respect to all variables. By using these these sufficient conditions we prove solvability in Holder classes of the initial-boundary value problems for the linearized Cahn-Hilliard equation with dynamic boundary conditions of two types. In addition, Schauders estimates are derived for the solutions corresponding to the problem under study.

引用

页码：391 / 429

页数：39