Abstract
In this paper we apply the method of implicit time discretization to the mean curvature flow equation including outer forces. In the framework ofBV-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.
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This work was supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 256, Bonn
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Luckhaus, S., Sturzenhecker, T. Implicit time discretization for the mean curvature flow equation. Calc. Var 3, 253–271 (1995). https://doi.org/10.1007/BF01205007
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DOI: https://doi.org/10.1007/BF01205007