Rate-Independence, Homogenization and Multiscaling

seminar: Mouvements of measures for optimal transportation problems

speaker: Giuseppe Buttazzo (Dipartimento di Matematica, Università di Pisa)

abstract: Starting from the work of Brenier where a dynamic formulation for optimal transportation problems was proposed, we investigate minimum problems of the form $$\min\Big\{\int₀¹ \Psi(\sigma)\,dt\ :\ -{\rm div\,}\sigma=f\Big\}$$ where $\Psi$ is a l.s.c. functional defined on measures. As an application we study the mouvement of a measure $\rho_t$ which satisfies the continuity equation $$\partial_t\rho+{\rm div}_x(\rho v)=0$$ and minimizes some suitable cost functional $F(\rho,v)$ assuming fixed values $ \rho_{t=0}=\rho0$ and $\rho_{{t=1}=\rho1$.} Some numerical computations are also provided, following the scheme proposed by Benamou and Brenier.

timetable:
Thu 15 Nov, 18:35 - 19:05, Sala Conferenze Centro De Giorgi
documents:

buttazzo.pdf

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