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New weighted sharp Trudinger–Moser inequalities defined on the whole euclidean space \( {\mathbb {R}}^N \) and applications

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A Correction to this article was published on 15 May 2023

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Abstract

In this paper, we provide an extension to the whole euclidean space \( {\mathbb {R}}^N,\ N \ge 2, \) of the Trudinger–Moser inequalities proved by Calanchi and Ruf (Nonlinear Anal 121:403–411, 2015) involving a logarithmic weight. The inequalities are new and highlight very well the importance of the presence of this type of weight. Next, we prove some version of the concentration-compactness principle due to P.L. Lions giving some new improvements of the Trudinger–Moser inequalities established in the first part of this work. In the light of this last result, we treat some elliptic quasilinear problems involving new type of exponential growth condition at infinity.

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Authors and Affiliations

  1. High Institute of Applied Mathematics and Informatics of Kairouan, University of Kairouan, Avenue Assad Iben Fourat, 3100, Kairouan, Tunisia

    Sami Aouaoui

  2. Faculty of Sciences of Monastir, University of Monastir, Avenue de l’environnement, 5019, Monastir, Tunisia

    Rahma Jlel

Authors
  1. Sami Aouaoui
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  2. Rahma Jlel
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Correspondence to Sami Aouaoui.

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Communicated by Andrea Malchiodi.

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Aouaoui, S., Jlel, R. New weighted sharp Trudinger–Moser inequalities defined on the whole euclidean space \( {\mathbb {R}}^N \) and applications. Calc. Var. 60, 50 (2021). https://doi.org/10.1007/s00526-021-01925-7

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