Il prossimo incontro del ciclo dei “Seminari di Analisi junior” si terrà martedì 12 novembre 2024 alle ore 15.00, nella Sala Professori 1° Livello. Di seguito, riportiamo i nomi dei due speaker e gli abstract dei loro talk.

Federico Luigi Dipasquale: An application of the Łojasiewicz retraction theorem to nematic liquid crystals
Abstract: The Łojasiewicz retraction theorem states that the zero set of a real-analytic function is a deformation retract of its neighbourhood. In the first part of this talk, I will sketch the proof of this theorem. Then, I will discuss an application to the study of the topological structure of the minimisers of the Landau-de Gennes energy for nematic liquid crystals in three dimensional, simply connected domains, under physically meaningful boundary conditions. Based on joint works with Adriano Pisante (Sapienza) and Vincent Millot (UPEC).

Alba Lia Masiello:  Here’s what you missed on the infinity-Laplacian Eigenvalue Problem
Abstract:  We will study the asymptotic behavior of the eigenvalues of the p-Laplacian as p tends to infinity, with particular attention to Robin, Dirichlet, and Neumann boundary conditions. In particular, we will introduce higher-order eigenvalues, and we will then focus on the second one. Finally, we will consider the limit as p goes to $+infty$ of the eigenvalue and eigenfunctions.
This is the second part of the seminar presented by Vincenzo Amato, entitled “The infinity-Laplacian Eigenvalue Problem”.

The talk is based on a joint work with Vincenzo Amato, Carlo Nitsch, and Cristina Trombetti.

On the optimal sets in Polya and Makai type inequalities

Abstract: 

In this talk we examine some shape functionals, introduced by Polya and Makai, involving the torsional rigidity and the first Dirichlet-Laplacian eigenvalue for bounded, open and convex sets of R^n. We establish new quantitative bounds, which give us key properties and information on the behavior of the optimizing sequences. In particular, we consider two kinds of reminder terms that provide information about the structure of these sequences, such as the thickness.

This is a joint work in collaboration with Vincenzo Amato and Nunzia Gavitone

Giovedì 14 Novembre alle 16,30 presso l’aula F la Dott.ssa Anastasia Molchanova (TU Wien), terrà un seminario dal titolo: