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arXiv · 2203.14181

On a sharp inequality of Adimurthi-Druet type and extremal functions

José Francisco de Oliveira·João Marcos do Ó
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Abstract

Our main purpose in this paper is to establish the existence and nonexistence of extremal functions for sharp inequality of Adimurthi-Druet type for fractional dimensions on the entire space. Precisely, we extend the sharp Trudinger-Moser type inequality in (Calc.Var.Partial Differential Equations, \textbf{52} (2015) 125-163) for the entire space. In addition, we perform the two-step strategy of Carleson-Chang together blow up analysis method to ensure the existence of maximizers for the associated extremal problems for both subcritical and critical regimes. We also present a nonexistence result under subcritical regime for some special cases.

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José Francisco de Oliveira, João Marcos do Ó. 2022-03-27. On a sharp inequality of Adimurthi-Druet type and extremal functions. https://doi.org/10.1007/s00526-023-02499-2

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