Global solutions to the volume-preserving mean-curvature flow

In this paper, we construct global distributional solutions to the volume-preserving mean-curvature flow using a variant of the time-discrete gradient flow approach proposed independently by Almgren et al. (SIAM J Control Optim 31(2):387–438, 1993 ) and Luckhaus and Sturzenhecker (Calc Var Partial D...

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Veröffentlicht in:	Calculus of variations and partial differential equations 2016-02, Vol.55 (1), p.1-23, Article 18
Hauptverfasser:	Mugnai, Luca, Seis, Christian, Spadaro, Emanuele
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Calculus of variations Calculus of Variations and Optimal Control Optimization Construction Control Curvature Gradient flow Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Partial differential equations Systems Theory Theoretical
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Zusammenfassung:	In this paper, we construct global distributional solutions to the volume-preserving mean-curvature flow using a variant of the time-discrete gradient flow approach proposed independently by Almgren et al. (SIAM J Control Optim 31(2):387–438, 1993 ) and Luckhaus and Sturzenhecker (Calc Var Partial Differ Equ 3(2):253–271, 1995 ).
ISSN:	0944-2669 1432-0835
DOI:	10.1007/s00526-015-0943-x