PhD research topic - Fabiana Leoni
Fully nonlinear equations, viscosity solutions, degenerate ellipticity, geometric equations
Qualitative properties of viscosity solutions of fully nonlinear degenerate elliptic equations: ABP maximum principle and Harnack inequality, regularity of solutions, sharp critical exponents in existence results, Liouville type theorems, spectral properties. Geometric evolution equations: level set approach to geometric flows, approximation results by reaction diffusion equations.
 M.Crandall, H. Ishii, P.L. Lions, "User's guide to viscosity solutions of second order partial differential equations", Bull. AMS 27 (1992), 1-67.
 L. Caffarelli, X. Cabre', "Fully nonlinear elliptic equations", AMS Colloquium Publications 43, AMS Providence, RI, 1995.