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

date	speaker	title	host(s)
January 21 (Departmental Colloquium: 4PM, B239)	Jun Kitagawa (Toronto)	Regularity theory for generated Jacobian equations: from optimal transport to geometric optics	Feldman
January 26
February 2	Jessica Lin (Madison)	TBA	Kim
February 9
February 16
February 17 (joint with Analysis Seminar: 4PM, B139)	Chanwoo Kim (Madison)	Hydrodynamic limit from the Boltzmann to the Navier-Stokes-Fourier	Seeger
February 23	Jennifer Beichman (Madison)	TBA	Kim
March 2	Benoit Pausader (Princeton)	TBA	Kim
March 9	Haozhao Li (University of Science and Technology of China)	TBA
March 16
March 23	Ben Fehrman (University of Chicago)	TBA	Lin
March 30	Spring recess Mar 28-Apr 5 (S-N)
April 6
April 13
April 20	Yuan Lou (Ohio State)	TBA	Zlatos
April 27
May 4

Abstracts

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.