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.
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.File in questo prodotto:
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