Equivalence of critical and subcritical sharp Trudinger–Moser inequalities in fractional dimensions and extremal functions
José Francisco de Oliveira
Federal University of Piauí, Teresina, BrazilJoão Marcos do Ó
Federal University of Paraíba, João Pessoa, Pb, Brazil
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Abstract
We establish critical and subcritical sharp Trudinger–Moser inequalities for fractional dimensions on the whole space. Moreover, we obtain asymptotic lower and upper bounds for the fractional subcritical Trudinger–Moser supremum from which we can prove the equivalence between critical and subcritical inequalities. Using this equivalence, we prove the existence of maximizers for both the subcritical and critical associated extremal problems. As a by-product of this development, we can explicitly calculate the value of the critical supremum in some special situations.
Cite this article
José Francisco de Oliveira, João Marcos do Ó, Equivalence of critical and subcritical sharp Trudinger–Moser inequalities in fractional dimensions and extremal functions. Rev. Mat. Iberoam. 39 (2023), no. 3, pp. 1073–1096
DOI 10.4171/RMI/1349