Preprint 34/2006

Remarks on the variational nature of the heat equation and of mean curvature flow

Giovanni Bellettini and Luca Mugnai

Contact the author: Please use for correspondence this email.
Submission date: 27. Mar. 2006
Pages: 26
Bibtex
MSC-Numbers: 49J45, 53C44, 35K10
Keywords and phrases: heat equation, space-time energy minimizers, mean curvature flow
Download full preprint: PDF (264 kB)

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 formula10 on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related formula10. We show some connections between minimizers of formula10 and mean curvature flow

07.06.2018, 02:11