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

[BibTeX]

Degree Thesis

Inserted: 13 jun 2017
Last Updated: 13 jun 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 perturbe the minimization algorithm of a functional $\phi$ in a metric space (S; d), introduced in the book "Gradient Flows in Metric Spaces and in the Space of Probability Measure" by L. Ambrosio, N.Gigli and G. Savarè, and prove that its minimizing movements are curves of maximal slope for $\phi$ with a perturbed velocity. We also show some cases in which the perturbed minimizing movements can escape from potential wells.


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