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Il 24 settembre alle 16, nell'aula B del Dipartimento di Matematica e 
Informatica (sede di via Ospedale), il

Prof. Luca Martinazzi 
dell'Università di Padova terrà un seminario intitolato

News on the Moser-Trudinger inequality: from sharp estimates to the 
Leray-Schauder degree

Abstract: The existence of critical points for the Moser-Trudinger 
inequality for large energies has been open for a long time. We will 
first show how a collaboration with G. Mancini allows to recast the 
Moser-Trudinger inequality and the existence of its extremals 
(originally due to L. Carleson and A. Chang) under a new light, based 
on sharp energy estimate. Building upon a recent subtle work of O. 
Druet and P-D. Thizy, in a work in progress with O. Druet, A. 
Malchiodi and P-D. Thizy, we use these estimates to compute the 
Leray-Schauder degree of the Moser-Trudinger equation (via a suitable 
use of the Poincaré-Hopf theorem), hence proving that for any bounded 
non-simply connected domain the Moser-Trudinger inequality admits 
critical points of arbitrarily high energy.

Tutti i docenti, i dottorandi e gli studenti interessati sono invitati 
a partecipare.