Multiplicity results for the Allen-Cahn equation

Abstract:
In this talk, we show multiplicity results for solutions of the Allen-Cahn equation on compact manifolds with boundary, for both Neumann and Dirichlet boundary conditions. By exploiting the Gamma-convergence of the Allen-Cahn functional to the perimeter functional, classical Lusternik-Schnirelmann and Morse theory, and some properties of the isoperimetric problem for small volumes in Riemannian manifolds, a lower bound on the number of solutions is given based on certain topological invariants of the underlying manifold.
These results stem from collaborative work with S. Nardulli (UFABC, Brazil), R. Olivier-Bonafoux (UNIVR, Italy), G. Orlandi (UNIVR, Italy), and P. Piccione (USP, Brazil).

Bio:
I earned my Ph.D. in Mathematics from the University of Camerino (Italy) in 2019.
After some fruitful experiences with a startup and university spin-off, I am currently a research assistant professor (RTDa) for the School of Science and Technology at the University of Camerino (Italy).
In the early years of my research journey, I worked on both Optimal Control Theory and Gesture Recognition.
Nowadays, my research is primarily focused on Mathematical Analysis, with particular emphasis on the study of Hamiltonian systems and Differential Geometry.

link zoom: https://univr.zoom.us/j/98531087229?pwd=UUVKZEd5T1NtK1hOci9MLzBpK0pTZz09

ID meeting: 985 3108 7229
Code: 985998

Referente DI: Giandomenico Orlandi