My research explores the interplay between non-linear partial differential equations and the calculus of variations. I am particularly interested in the study of non-local elliptic operators, investigating how boundary conditions dictate the existence, regularity, and qualitative behavior of solutions. My work leverages diverse analytical techniques ranging from critical point theory for existence results to the development of sharp geometric and functional inequalities to characterize the underlying functional spaces and establish regularity in non-smooth settings.
Maz'ya-type bounds for sharp constants in fractional Poincaré-Sobolev inequalities, with F. Bozzola. Calculus of Variations and Partial Differential Equations (2025, accepted). [ARXIV]
On a fractional semilinear Neumann problem arising in Chemotaxis, with E. Cinti. Journal of Differential Equations, Vol. 452 (2026), 113779. [DOI]
A multiplicity result for a double perturbed Schrödinger-Bopp-Podolsky-Proca system. Journal of Mathematical Analysis and Applications, Vol. 540, Issue 2 (2024), 128648. [DOI]
Barycentric stability of nonlocal perimeters: the convex case, with C. Gambicchia, E. M. Merlino, and B. Ruffini. Preprint (2025). [ARXIV]
ORCID ID- https://orcid.org/0009-0006-4340-2386