# Generated Jacobian equations and regularity: optimal transport, geometric optics, and beyond

Thursday, October 6, 2016 -

4:30pm to 6:00pm

PLEASE NOTE SPECIAL DAY, TIME AND LOCATION. Equations of Monge-Amp{\`e}re type arise in numerous contexts, and solutions often exhibit very subtle properties; due to the highly nonlinear nature of the equation, and its degenerate ellipticity. Motivated by an example from geometric optics I will talk about the class of Generated Jacobian Equations, recently introduced by Trudinger. This class includes optimal transport, the Minkowski problem, and the classical Monge-Amp{\`e}re equation. I will present a new regularity result for weak solutions of these equations, which is new even in the case of equations arising from near-field problems in geometric optics. This talk is based on joint works with Nestor Guillen.

Speaker:

Jun Kitagawa

Michigan State University

Event Location:

Fine Hall 1001