Equivalence of critical and subcritical sharp Trudinger–Moser inequalities in fractional dimensions and extremal functions

• José Francisco de Oliveira ^[2] ; João Marcos do Ó ^[1]
  1. [1] Universidade Federal da Paraíba

     Universidade Federal da Paraíba

     Brasil

     
  2. [2] Federal University of Piauí, Teresina, Brazil
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 3, 2023, págs. 1073-1096
• Idioma: inglés
• DOI: 10.4171/RMI/1349
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• Resumen

  • 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