Calculus of Variations and Geometric Measure Theory
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A. Tribuzio

Perturbations of Minimizing Movements and Curves of Maximal Slope

created by tribuzio on 13 Jun 2017
modified on 26 Apr 2018


Accepted Paper

Inserted: 13 jun 2017
Last Updated: 26 apr 2018

Year: 2017

The topics discussed in this paper are a reworking of those contained in a part of my master thesis. For this, I thank the professor Andrea Braides, my advisor, for his careful help and his ideas that made this work possible.


We modify the De Giorgi's minimizing movements scheme for a functional, by perturbing the dissipation term, and find a condition on the perturbations which ensures the convergence of the scheme to an absolutely continuous perturbed minimizing movement. The perturbations produce a variation of the metric derivative of the minimizing movement. This process is formalized by the introduction of the notion of curve of maximal slope with a given rate. We show that if we relax the condition on the perturbations we may have many different meaningful effects; in particular, some perturbed minimizing movements may explore different potential wells.


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