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Existence and nonexistence of maximizers for variational problems associated with Trudinger–Moser type inequalities in \({\mathbb{R}^N}\)

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Abstract

We discuss the existence of a maximizer for a maximizing problem associated with the Trudinger–Moser type inequality in \({\mathbb{R}^N(N\geq 2)}\). Different from the bounded domain case, we obtain both of the existence and the nonexistence results. The proof requires a careful estimate of the maximizing level with the aid of normalized vanishing sequences.

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  1. Department of Industrial System, Faculty of Symbiotic Systems Science, Fukushima University, 1 Kanayagawa, Fukushima, 960-1296, Japan

    Michinori Ishiwata

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  1. Michinori Ishiwata
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Correspondence to Michinori Ishiwata.

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Ishiwata, M. Existence and nonexistence of maximizers for variational problems associated with Trudinger–Moser type inequalities in \({\mathbb{R}^N}\) . Math. Ann. 351, 781–804 (2011). https://doi.org/10.1007/s00208-010-0618-z

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  • DOI: https://doi.org/10.1007/s00208-010-0618-z

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