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, December 16
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.