Convergence of the Phase-Field Equations to the Mullins-Sekerka Problem with Kinetic Undercooling

  • H. M. Soner


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 i, the limiting interface is (d — l)-rectifiable with a square-integrable mean-curvature vector.


Weak Solution Maximum Principle Heat Equation Heat Kernel Radon Measure 
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© Springer-Verlag Berlin Heidelberg 1999

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  • H. M. Soner

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