## Diff. Geom, Math. Phys., PDE Seminar: Luca Martinazzi

- Date: 04/10/2018
- Time: 15:30

University of British Columbia

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

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.

Location and time: MATH 225 3:30pm-4:30pm