Main research fields

Partial differential equations in natural science, mathematical finance and geometry

More specifically...

My research focuses on problems related to nonlinear elliptic and parabolic partial differential equations. My interests have been originally devoted to the study of the existence, uniqueness and regularity of viscosity solutions to fully nonlinear degenerate elliptic and parabolic equations with applications in stochastic and deterministic optimal control problems, in homogenization problems and in some front propagations problems arising in many fields of Physics, Engineering, Biology and Material Science. During the last years I have been interested also in local and nonlocal geometric-analysis PDEs arising in variational problems. These type of equations offer new technical and conceptual challenges due to the coupling of both the non-linearity and the non-locality.