Analysis Seminar

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Monge Ampere equation and unique continuation for differential inclusions

Speaker: Guido De Philippis, Courant Institute

Location: Warren Weaver Hall 1302

Date: Thursday, February 8, 2024, 11 a.m.

Synopsis:

The Monge Ampere equation is a prototypical non-linear equation arising in several questions concerning Geometry, Optimal Design, Optimal transport, etc. I will review some of the applications and some of the known results, in particular concerning the Sobolev regularity of the solutions. 

I will then show how, in 2 dimensions, these results have an equivalent formulation in terms of a unique continuation property for solutions of differential inclusions, and use this link to reprove the Sobolev regularity result for planar solutions of the MA equation obtained by Figalli Savin and myself in 2013. This is a joint work with Andre Guerra and Riccardo Tione.