Optimal Transportation and Nonlinear Elliptic PDE

MINI-COURSE IN GEOMETRIC PDE
Topic:Optimal Transportation and Nonlinear Elliptic PDE
Speaker:Neil Trudinger
Affiliation:Australian National University and Member, School of Mathematics
Date:Tuesday, November 11
Time/Room:1:30pm - 3:30pm/S-101

In these lectures we will describe the relationship between optimal transportation and nonlinear elliptic PDE of Monge-Ampere type, focusing on recent advances in characterizing costs and domains for which the Monge-Kantorovich problem has smooth diffeomorphism solutions. Background references. L. C. Evans, PDE and Monge-Kantorovich mass transfer. Current developments in Mathematics, 1997. Int. Press, Boston, (1999). R. T. Rachev and L. Ruschendorf, Mass transportation problems, Springer, 1998. J. Urbas, Mass transfer problems, Lecture Notes, Univ. of Bonn, 1998. C. Villani, Topics in optimal transportation, Amer. Math. Soc. 2003.