Nonlinear analysis, nonlinear PDE, critical point theory, variational methods.
My primary research interest is focused in the study of nonlinear partial differential equations. In particular:
- Existence of the solutions.
- Quasilinear elliptic equations.
- Fully nonlinear uniformly elliptic equations.
- Geometric and qualitative properties of the solutions.
- Hardy potential.
- Liouville type theorems.
- Local and global existence of solutions to the nonlinear p-heat equation.
- Finite speed of propagation and extinction in finite time.
- Moving plane method; p-Laplacian operator.
- Nonlocal problems.
- Higher order nonlocal problems.
- Singularly perturbed elliptic problems.
- Singular problems.
- Semilinear elliptic equations.
- Supercritical problems.
During the Ph.D. studies (at ‘Universidad Autonoma de Madrid (Madrid, Spain)’ and ‘SISSA (Trieste, Italy)’) I worked on perturbative problems and in particular on the Concentration and asymptotic behavior of solutions for singularly perturbed mixed problems.
Teaching - Academic Year 2019/2020:
- MATEMATICA PER L'ANALISI DEI DATI (CdS in Informatica)
- EQUAZIONI ALLE DERIVATE PARZIALI (CdS Magistrale in Matematica)
- ANALISI MATEMATICA 1 MODULO 1 (CdS in Ingegneria Meccanica)
- MODELLISTICA PER PROBLEMI DIFFERENZIALI (CdS in Ingegneria Meccanica)