Phase field model with a variable chemical potential

We study some asymptotic behaviour of phase interfaces with variable chemical potential under the uniform energy bound. The problem is motivated by the Cahn-Hilliard equation, where one has a control of the total energy and chemical potential. We show that the limit interface is an integral varifold with generalized L-P mean curvature. The convergence of interfaces as epsilon --> 0 is in the Hausdorff distance sense.