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

  • H. M. Soner

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

Keywords

Weak Solution Maximum Principle Heat Equation Heat Kernel Radon Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

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  • H. M. Soner

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