Research
Research Overview
My research is on nonlinear elliptic partial differential equations. Current research topics include:
- Homogenization of Hamilton-Jacobi equations, non-divergence structure elliptic equations, free boundary problems, fully nonlinear elliptic equations
- The Convex Envelope: the derivation of a PDE satisfied by the convex envelope, the numerical solution of the equation, and the analysis of the Dirichlet problem.
- Numerical Methods for the Monge-Ampere equation
- Finite Difference Methods for Nonlinear Elliptic PDEs
- Motion by Mean Curvature
- Infinity Laplacian
- Stochastic Control Interpretation of PDEs