Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential

Abstract

In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the $L^p$ type estimates and the theory of Morrey spaces, we prove the Hölder continuity of the solutions. Then we obtain the existence of global classical solutions. The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.