Wednesday, May 6, 2026 — 2:30 pm — aula M1.6, edificio Matematica
A priori bounds for planar elliptic equations and systems
Abstract: I will discuss some recent results concerning uniform a priori estimates for positive solutions of elliptic equations and semilinear Hamiltonian elliptic systems involving exponential-type non-linearities in dimensions two. These topics are presented in joint works in collaboration with Laura Baldelli (Karlsruhe Institute of Technology), Luca Battaglia (Università degli Studi Roma Tre), Giulio Romani (Università degli Studi di Udine) and Pierre-Damien Thizy (Université Claude Bernard Lyon 1). In the case of systems, we consider a broad class of coupled nonlinearities with asymptotic critical behaviour in the sense of Brezis-Merle. The approach we follow is based on a blow-up analysis combined with Liouville-type theorems and integral estimates. As a consequence of our a priori estimates, we prove the existence of a positive solution by means of Fixed Point Index theory.