PDE Geometric Analysis seminar
The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
Seminar Schedule Spring 2015
|January 21 (Departmental Colloquium: 4PM, B239)||Jun Kitagawa (Toronto)||Regularity theory for generated Jacobian equations: from optimal transport to geometric optics||Feldman|
|February 2||Jessica Lin (Madison)||TBA||Kim|
|February 23||Jennifer Beichman (Madison)||TBA||Kim|
|March 2||Benoit Pausader (Princeton)||TBA||Kim|
|March 30||Spring recess Mar 28-Apr 5 (S-N)|
|April 20||Yuan Lou (Ohio State)||TBA||Zlatos|
Jun Kitagawa (Toronto)
Regularity theory for generated Jacobian equations: from optimal transport to geometric optics
Equations of Monge-Ampere type arise in numerous contexts, and solutions often exhibit very subtle qualitative and quantitative properties; this is owing to the highly nonlinear nature of the equation, and its degeneracy (in the sense of ellipticity). Motivated by an example from geometric optics, I will talk about the class of Generated Jacobian Equations; recently introduced by Trudinger, this class also encompasses, for example, optimal transport, the Minkowski problem, and the classical Monge-Ampere 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 reflector problems (of interest from a physical and practical point of view). This talk is based on joint works with N. Guillen.