Convergence of the phase field equations to the Mullins-Sekerka problem with kinetic undercooling

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."