In this talk, I will introduce the special Lagrangian and Lagrangian mean curvature equations.
I will discuss some recent developments on a priori- estimates, regularity, and the existence of solutions of Lagrangian mean curvature type equations and their applications.
I will also mention some recent results on the regularity of solutions of fourth order PDEs, which are critical points of variational integrals of the Hessian of a scalar function. Examples include volume functionals on Lagrangian submanifolds.
University of Washington