Convergence of phase-field approximations to the Gibbs�Thomson law

R�ger, Matthias; Tonegawa, Yoshihiro
May 2008
Calculus of Variations & Partial Differential Equations;May2008, Vol. 32 Issue 1, p111
Academic Journal
We prove the convergence of phase-field approximations of the Gibbs�Thomson law. This establishes a relation between the first variation of the Van der Waals�Cahn�Hilliard energy and the first variation of the area functional. We allow for folding of diffuse interfaces in the limit and the occurrence of higher-multiplicities of the limit energy measures. We show that the multiplicity does not affect the Gibbs�Thomson law and that the mean curvature vanishes where diffuse interfaces have collided. We apply our results to prove the convergence of stationary points of the Cahn�Hilliard equation to constant mean curvature surfaces and the convergence of stationary points of an energy functional that was proposed by Ohta�Kawasaki as a model for micro-phase separation in block-copolymers.


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