PhD research topic - Fabiana Leoni

Fabiana Leoni

Research areas

Nonlinear PDEs


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.


[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.

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