José Francisco de Oliveira, João Marcos do Ó
Published 2022-03-27Version 1
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.
A sharp Trudinger-Moser type inequality involving $L^{n}$ norm in the entire space $\mathbb{R}^{n}$
Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two
A sharp inequality for the Strichartz norm
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