CDS/CIMMS Lunchtime Seminar: Hidden convexity in some geometric nonlinear PDEs

Yann Brenier, CNRS, Universite de Nice

We review few examples of nonlinear PDEs coming from geometry or physics for which a hidden convex structure can be exhibited. Robust existence and uniqueness results follow in a natural way once this structure is revealed. Among the examples we would like to discuss, feature the Monge-Ampere equation (and the related Minkowski and Monge problems), the Euler equations for incompressible fluids and the nonlinear electromagnetism of Born and Infeld.