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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.