A priori estimates for special Lagrangian equations
A priori estimates for special Lagrangian equations

Micah Warren, University of Washington
Fine Hall 314
We discuss recent a priori interior Hessian estimates for solutions of the special Lagrangian equation, when the equation has phase at least a certain value, or when the solution is convex. These equations include the sigma2 equation in dimension three. The gradient graph of any solution is a minimizing Lagrangian surface. While Heinz showed in the 50's that similar estimates hold for the sigma2 (MongeAmpere) equation in dimension two, Pogorelov showed that such estimates cannot hold for the sigma3 (MongeAmpere) equation in dimension three. This is joint work with Yu Yuan, partly also with Jingyi Chen.