Hessian Estimates for the Lagrangian mean curvature equation

In this talk, we will derive a priori interior Hessian estimates for the Lagrangian mean curvature equation under certain natural restrictions on the Lagrangian phase. As an application, we will use these estimates to solve the Dirichlet problem for the Lagrangian mean curvature equation with continuous boundary data on a uniformly convex, bounded domain.