Recently Added

Geometric PDE - Optimal transportation and nonlinear elliptic PDE

Neil Trudinger
Institute for Advanced Study
November 11, 2008


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).

Geometric PDE - Variational techniques for the prescribed Q-curvature equation

Andrea Malchiodi
Institute for Advanced Study
October 21, 2008


After recalling the definition of Q-curvature and some applications, we will address the question of prescribing it through a conformal deformation of the metric. We will address some compactness issues, treated via blow-up analysis, and then study the problem, which has variational structure, using a Morse-theoretical approach.