Ημερομηνία: Παρασκευη 14 Ιουνίου 2024
Ώρα: 15:00
Τόπος: Α21
Oμιλητής: Dr. Dimitrios Gazoulis, University of Athens
Τίτλος:A Pointwise Gradient bound for Pucci's equations and it's consequences
Περίληψη: We consider Pucci's extremal operators in $ \mathbb{R}^n $ and study entire solutions of the respective Pucci's equations. In this talk, we will prove a pointwise gradient estimate that generalizes the Modica inequality for fully nonlinear elliptic equations. This bound is sharp, in the sense that, when equality is attained at some point, then the level sets of the solutions will be hyperplanes. We will also provide some applications, such as Liouville theorems and Harnack-type inequalities.