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Abstract or Table of Contents
Abstract: "I prove that the solutions of the phase field equations, on a subsequence, converge to a weak solution of the Mullins-Sekerka problem with kinetic undercooling. The method is based on energy estimates, a monotonicity formula, and the equipartition of the energy at each time. I also show that the limiting interface is (d-1)- rectifiable for almost all t with a square integrable mean curvature vector."