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 subseque nce, converge to a weak solution of the Mullins-Sekerka problem with k inetic undercooling. The method is based on energy estimates, a monoto nicity formula, and the equipartition of the energy at each time. I al so show that for almost all t, the limiting interface is (d - 1)-recti fiable with a square-integrable mean-curvature vector.