Seminar
Reverse Faber-Krahn inequality for a truncated Laplacian operator
Department's Seminar
Series:
18 April 2023
Start time
2:30 pm
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room "1"
Target audience:
University community
UniTrento students
Attendance:
Free
Contact person:
Andrea Pinamonti, Andrea Marchese, Giorgio Saracco
Contact details:
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 04 61/281508-1625-1701-3786-1980-1511
Speaker:
Enea Parini (Aix-Marseille Université)
Abstract
In this talk we will consider a reverse Faber-Krahn inequality for the principal eigenvalue $\mu_1(\Omega)$ of the fully nonlinear operator
\[ \mathcal{P}_N^+ u := \lambda_N(D^2 u), \]
where $\Omega \subset \mathbb{R}^N$ is a bounded, open convex set, and $\lambda_N(D^2 u)$ is the largest eigenvalue of the Hessian matrix of $u$. The result will be a consequence of the isoperimetric inequality
\[ \mu_1(\Omega) \leq \frac{\pi^2}{\text{diam}(\Omega)^2}. \]
Moreover, we will discuss the minimization of $\mu_1$ under various kinds of constraints. The results have been obtained in collaboration with Julio D. Rossi and Ariel Salort (Buenos Aires).
Past events
Pleas visit the web page of Analysis Seminars