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Implicit time discretization for the mean curvature flow equation. (English) Zbl 0821.35003
Summary: We apply the method of implicit time discretization to the mean curvature flow equation including outer forces. In the framework of BV-functions we construct discrete solutions iteratively by minimizing a suitable energy- functional in each time step. Employing geometric and variational arguments we show an energy estimate which assures compactness of the discrete solutions. An additional convergence condition excludes a loss of area in the limit. Thus existence of solutions to the continuous problem can be derived. We append a brief discussion of the related Mullins-Sekerka equation.

MSC:
35A15 Variational methods applied to PDEs
49Q20 Variational problems in a geometric measure-theoretic setting
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