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

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

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Jun Kitagawa, Michigan State University
Fine Hall 1001

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.