Il giorno Martedì 16 Aprile 2024, alle ore 14:30 nella Sala Professori I Livello del DMA, il Dott. Davide Carazzato della Scuola Normale Superiore di Pisa, terrà il seguente seminario:

Davide Carazzato (SNS Pisa)

Titolo: “Existence of minimizing sets for weakly repulsive interaction energies”

Abstract: In this seminar we will present an existence result for minimizing sets for some non-local
interaction energies. Specifically, we consider a weakly repulsive Riesz-like energy, and we
study the minimization in two settings: in the space of probabilities and, differently, in the
class of densities with an L^infty bound and an L^1 constraint. The regularity of the kernel
allows us to compare the probability minimizers with the L^infty ones when the L^1
constraint is small. Heuristically, if the probability minimizers are singular, we can prove the existence of
minimizing sets whenever the L^1 constraint is small. This seminar is based on a joint work
with Aldo Pratelli and Ihsan Topaloglu.