Incontri di Analisi Matematica tra Firenze, Pisa e Siena
MathAnalysis(at)UniFIPISI, V
mercoledì 6 dicembre 2023
Università degli Studi di Firenze
Dipartimento di Matematica e Informatica “Ulisse Dini” (DiMaI)
La partecipazione è libera, ti chiediamo però di compilare il modulo di registrazione
PROGRAMMA
14:30 apertura
14:35 Alessandra Lunardi (Università di Parma): Sobolev and BV functions in infinite dimension
15:30 Masayuki Hayashi (Università di Pisa): Modified energies for the generalized derivative NLS
16:00 pausa caffè
16:30 Luigi C. Berselli (Università di Pisa): Energy conservation for incompressible viscous fluids
17:25 Giorgio Saracco (Università di Firenze): Bijections between isoperimetric sets, prescribed curvature sets, and p-Cheeger sets
17:55 chiusura
ABSTRACTS
Luigi C. Berselli: In this talk I will discuss classical and recent results about the energy conservation for Leray-Hopf solutions to the Navier-Stokes equations, satisfying additional assumptions.
In particular, I will focus on Hölder continuous solutions (wrt space variables) and on the technical steps necessary to pass from the periodic case to the Dirichlet problem in various domains with solid boundaries.
Joint work with A. Kaltenbach and M. Růžička
Alessandra Lunardi: In Hilbert or even Banach spaces
As in finite dimension, Sobolev and BV functions are tools for the study of different problems, in particular of PDEs with infinitely many variables, arising in mathematical physics in the modeling of systems with an infinite number of degrees of freedom, and of stochastic PDEs through Kolmogorov equations.
In this talk I will describe some of the main features and open problems concerning such function spaces.
Masayuki Hayashi: We prove global existence of solutions to the generalized derivative nonlinear Schrödinger equation in
This talk is based on a joint work with T. Ozawa and N. Visciglia.
Giorgio Saracco: Bijections between isoperimetric sets, prescribed curvature sets, and p-Cheeger sets
Given a planar, open set
We shall see that there exist bijections
As a byproduct we infer some convexity properties on the isoperimetric profile, and some fine regularity properties on the contact surface of minimizers.
Based on joint works with Caroccia, Leonardi, Neumayer, and Pratelli.