Calculus of Variations and Geometric Measure Theory

G. Bellettini - L. Mugnai

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

created by belletti on 14 Mar 2006
modified on 24 Mar 2006



Inserted: 14 mar 2006
Last Updated: 24 mar 2006

Year: 2006


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 $\mathcal F$ on the class of space-time tracks of moving hypersurfaces, and we relate minimizers of $\mathcal F$ to solutions of mean curvature flow.