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 07 Jan 2020


Published Paper

Inserted: 13 jun 2017
Last Updated: 7 jan 2020

Journal: Networks and Heterogeneous Media
Volume: 13
Number: 3
Pages: 423-448
Year: 2017
Doi: 10.3934/nhm.2018019

The topics discussed in this paper are a reworking of those contained in part of my master thesis. Thus, I thank Professor Andrea Braides 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.

Keywords: Gradient flows, minimizing movements, perturbations

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