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 Jul 2017

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Preprint

Inserted: 13 jun 2017
Last Updated: 26 jul 2017

Year: 2017
Notes:

The topics discussed in this paper are a reworking of a part of my Master thesis "Perturbazioni di movimenti minimizzanti e curve di massima pendenza" through which I obtain a Master Degree in "Matematica Pura e Applicata" at the university of Rome "Tor Vergata". For this work therefore I would like to thank the Professor Andrea Braides, my thesis advisor, for his help and willingness that were fundamental for the success of this work.


Abstract:

We will consider a perturbation of the De Giorgi's minimization algorithm of a functional defined in a complete metric space, introduced by Ambrosio, Gigli and Savarè, obtained multiplying positive coefficients (depending on time discretization scale and on the step of the algorithm) to the dissipation. We will find a condition on the perturbations which ensures the convergence of the scheme and that the "perturbed" minimizing movements are a kind of curves of maximal slope for the functional with a perturbed velocity. Moreover, we will show some cases in which the condition over the perturbations are relaxed and this brings some interesting effects, in particular some perturbed minimizing movements can escape from potential wells.


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