News on the Moser-Trudinger inequality -- Luca Martinazzi (Università di Padova)

Seminario di: Analisi Matematica

Dettagli dell'evento


dalle 16:00 alle 17:00


Aula B1, Palazzo Manfredini

Persona di riferimento

Lorenzo Brasco

Aggiungi l'evento al calendario

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. In a work in progress with F. De Marchis, O. Druet, A. Malchiodi and P-D. Thizy, we expect to use a variational argument to treat the case of a closed surface.

archiviato sotto: