Workshop: Nonlinear models and analysis, 20/05-24/05, 2002

Title: Optimal Current Transportation: from Monge to Maxwell

Speaker: Yann Brenier, CNRS Nice, on leave from Paris 6

Abstract:
Monge addressed the problem of optimal mass transportation more than two centuries ago. In PDE terms, this problem is linked to both the Monge-Ampere equation and the Eikonal equation. In the limit of almost uniform mass density, optimal mass transportation reduces to classical Electrostatics, involving the (linear) Poisson equation. Therefore, it is natural to look for an optimal transportation theory from which classical Electrodynamics could be derived in a similar way. Such a theory can be constructed from the concept of extremal surfaces, leading to nonlinear hyperbolic linearly degenerate systems of conservation laws, closely related to the Born-Infeld nonlinear theory of the electromagnetic field.