10/12/2007

Yu Yuan
Washington University

Hessian and gradient estimates for special Lagrangian equations

We derive Hessian and gradient estimates for 3-d special Lagrangian equations of phase at least a critical value, including the sigma-2 equation in dimension three. The gradient graph of the solutions are minimal Lagrangian surfaces. An Hessian estimate for the sigma-2 (Monge-Ampere) equation in dimension two was obtained by Heinz in the 1950's, and irregular solutions to the sigma-3 (Monge-Ampere) equation in dimension three were constructed by Pogorelov in the 1970's. This is joint work with Micah Warren.