Convergence of the phase-field equations to the mullins-sekerka problem with kinetic undercooling

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 for almost all t, the limiting interface is (d – 1)-rectifiable with a square-integrable mean-curvature vector.Dedicated to Mort Gurtin on the occasion of his sixtieth birthday