Hello I am Adrian.
I am interested in the regularity theory of the Monge-Ampere equation. The theory started with a series of papers by Caffarelli in the early 1990s. I will try to work through the papers to learn some basic techniques for studying the Monge-Ampere equation and nonlinear elliptic PDEs.
1. Caffarelli, Some regularity properties of solutions of Monge Ampere equation, Comm. Pure Appl. Math, 1991.
2. Caffarelli, A localization property of viscosity solutions to the Monge-Ampere equation and their strict convexity, Ann. of Math , 1990.
3. Caffarelli, The regularity of mappings with a convex potential, J. Amer. Math Soc., 1992.