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Seminario di Equazioni Differenziali e Applicazioni: “Improved Adams-type inequalities and their extremals in dimension 2m”

Giovedì 3 Maggio 2018, ore 14:30 - Aula 2BC30 - Gabriele Mancini

ARGOMENTI: Seminari

Giovedì 3 Maggio 2018 alle ore 14:30 in Aula 2BC30, Gabriele Mancini (Università di Padova) terrà un seminario dal titolo “Improved Adams-type inequalities and their extremals in dimension 2m”.

Abstract
This talk focuses on Moser-Trudinger type inequalities and on the existence of critical points for the corresponding exponential-type energy functionals. In particular, I will present the proof of the existence of maximizers for the Adams inequality (which is a high-order version of the MT inequality) on even-dimensional bounded smooth domains. I will also discuss an alternative approach in dimension 2 based on sharp energy estimates for blowing-up sequences of critical points. Such estimates describe how the existence of extremals is affected by perturbations of the exponential nonlinearity and suggest how to construct a family of MT-type functionals for which extremals do not exist.
These results were obtained in collaboration with Azahara De La Torre, Luca Martinazzi e Pierre-Damien Thizy.

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