Sharp regularity theory for singular fully nonlinear PDEs

In this talk I will present some recent results on sharp gradient estimates for viscosity solutions to certain fully non-linear PDEs
with singular potentials.
The general results do not assume sign
constraints, thus associated free boundary problems may have two-phases.
At the end, I will dicuss a class of fully nonlinear
singularly perturbed PDEs that can be interpreted as a non-variational Alt-Caffarelli theory.

web.mate.polimi.it/cdv/