### Speaker: David Stolnicki

### La Sapienza University of Rome, Italy

### Date: Tuesday, October 27, 2022 at 2 p.m. Santiago time

**Abstract:** In joint work with F. Pacella, we study the existence and asymptotic behavior of radial positive solutions of some fully nonlinear equations involving Pucci’s extremal operators in dimension two and higher. In particular we prove the existence of a positive solution of a fully nonlinear version of the Liouville equation in the plane. Moreover, for the (negative) Pucci P^- operator, we show the existence of a critical exponent and give bounds for it. The same technique is then applied in higher dimensions to improve the previously known bounds.

**Venue:** Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851

**Chair:** Gabrielle Nornberg