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Nonlinear Analysis

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

Luca Martinazzi, University of Padova

Location:  Hill 705
Date & time: Tuesday, 01 May 2018 at 1:40PM - 2:40PM

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 PoincarĂ©-Hopf theorem), hence proving that for any bounded non-simply connected domain the Moser-Trudinger inequality admits critical points of arbitrarily high energy.

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