An L∞ bound for solutions of a fractional Cahn–Hilliard equation

Abstract Recently, some fractional Cahn–Hilliard equations are proposed for phase transition and image process, etc., which have attracted a lot of attention. In this paper, we concern the L ∞ bound of the solutions to a class of fractional Cahn–Hilliard equations, which extends the results of integer order. By an invariant derivative technique, the crucial uniform estimates related to the kernel function of fractional Cahn–Hilliard are established. The technique presented here can be also applied to the other related fractional models.