We show that the classical solution of the heat equation can be seen as the minimizer of a suitable functional defined in space-time. Using similar ideas, we introduce a functional F on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related with F. We show some connections between minimizers of F and mean curvature flow.

Bellettini, G., Mugnai, L. (2008). Some aspect of the variational nature of mean curvature flow. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 10(4), 1013-1036.

Some aspect of the variational nature of mean curvature flow

BELLETTINI, GIOVANNI;
2008-01-01

Abstract

We show that the classical solution of the heat equation can be seen as the minimizer of a suitable functional defined in space-time. Using similar ideas, we introduce a functional F on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related with F. We show some connections between minimizers of F and mean curvature flow.
2008
Bellettini, G., Mugnai, L. (2008). Some aspect of the variational nature of mean curvature flow. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 10(4), 1013-1036.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1017390