Paolo Luzzini (Università degli Studi di Padova)

Thursday, March 2, 2023 — 12:00 pm — aula M1.7 edificio Matematica

Grushin eigenvalues: shape sensitivity and optimization

Abstract: It is well known that among all domains of a fixed volume, the ball minimizes the first eigenvalue of the Dirichlet Laplacian. The counterpart of this result for the Grushin Laplacian is instead an open problem. In this talk I will present some results in the direction of understanding such a problem.

I will first consider the shape sensitivity of Grushin eigenvalues on general domains with the aim of characterizing critical domains under isovolumetric and isoperimetric perturbations.

Next I will pass to the case of cartesian product domains, showing that in this class the first eigenvalue admits a unique minimizer and providing some estimates on the minimum. Finally I will discuss some numerical experiments and some open problems.

The talk is based on joint works with Pier Domenico Lamberti (Università degli Studi di Padova), Paolo Musolino (Università Ca’ Foscari Venezia), Luigi Provenzano (Sapienza Università di Roma), and Joachim Stubbe (EPFL).