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02-02-17. Seminari d'edps i aplicacions. Fernando Charro (UPC) "The Monge-Ampere equation: Classical local applications and recent nonlocal developments" 15 h., Aula S01, FME-UPC

ABSTRACT:
In this talk we will present the classical local Monge-Ampere equation and some of its applications to optimal transport and differential geometry (Gaussian curvature). We will discuss the degeneracy of the equation and the challenges it poses for regularity of solutions. Finally, we will consider a nonlocal analogue of the Monge-Ampere operator, recently introduced in a joint work with Luis Caffarelli, and discuss future directions