Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential (Communications in Mathematical Research, 2021)
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 theHölder continuity of the solutions. Then we obtain the existence of global classicalsolutions. The present work can be viewed as an extension to the previous work onthe Cahn-Hilliard equation with concentration dependent mobility and potential.