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A new Trudinger–Moser type inequality and an application to some elliptic equation with doubly exponential nonlinearity in the whole space \( {\mathbb {R}}^2 \)

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Abstract

In this article, we establish a new Trudinger–Moser type inequality for radial functions in some appropriate weighted Sobolev space defined in the whole space \( {\mathbb {R}}^2. \) This inequality is used in order to study some elliptic equation defined in \({\mathbb {R}}^2\) and involving a nonlinearity with doubly exponential growth at infinity.

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Authors and Affiliations

  1. Institut Supérieur des Mathématiques Appliquées et de l’Informatique de Kairouan, Avenue Assad Iben Fourat, 3100, Kairouan, Tunisie

    Sami Aouaoui

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  1. Sami Aouaoui
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Correspondence to Sami Aouaoui.

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To the memory of my dear friend Professor Mohamed Benrhouma.

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Aouaoui, S. A new Trudinger–Moser type inequality and an application to some elliptic equation with doubly exponential nonlinearity in the whole space \( {\mathbb {R}}^2 \). Arch. Math. 114, 199–214 (2020). https://doi.org/10.1007/s00013-019-01386-7

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  • DOI: https://doi.org/10.1007/s00013-019-01386-7

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