Calculus of Variations and Geometric Measure Theory

S. Di Marino

Trasporto ottimo e problemi di evoluzione per sistemi di particelle

created by dimarino on 21 Jun 2012


Degree Thesis

Inserted: 21 jun 2012
Last Updated: 21 jun 2012

Year: 2011


The thesis is divided in three sections: the first one is devoted to the classical Optimal Transport Theory in general metric spaces with emphasis on the case of $X=Y=\mathbb{R}$, stressing the fact that the resulting metric space with the 2-Wasserstein distance is isometric with a cone in $L^2[0,1]$ and so many Hilbertian theories can be applied.
The second part is a self contained treatement of Hilbertian gradient flow in case of a convex lower semicontinuous function.
The third part is an application of the two previous section to the SPS (Sticky Particle System), due to Natile and Savaré.

Keywords: Optimal transport, Gradient Flow, Sticky Particle System