PhD research topic - Fabiana Leoni
Research areas
Nonlinear PDEs
Keywords
Fully nonlinear equations, viscosity solutions, degenerate ellipticity, geometric equations
Research topics
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.
Bibliography
[1] 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.
[2] L. Caffarelli, X. Cabre', "Fully nonlinear elliptic equations", AMS Colloquium Publications 43, AMS Providence, RI, 1995.