Year: 2020
Type: article
Abstract: In this paper, we are interested in several questions raised mainly in [17]. We consider the perturbed Moser-Trudinger inequality $I\_α^g(Ω)$ below, at the critical level $α=4π$, where $g$, satisfying $g(t)\to 0$ as $t\to +\infty$, can be seen as a perturbation with respect to the original case $g\equiv 0$. Under some additional assumptions, ensuring basically that $g$ does not oscillates too fast as $t\to +\infty$, we identify a new condition on $g$ for this inequality to have an extremal. This condition covers the case $g\equiv 0$ studied in [3,12,23]. We prove also that this condition is sharp in the sense that, if it is not satisfied, $I\_{4π}^g(Ω)$ may have no extremal.
Source: Analysis & PDE
Author: Pierre-Damien Thizy
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2787791395