Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups

Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan

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1 Citation (Scopus)

Abstract

In this paper, we prove the fractional logarithmic Sobolev inequality on homogeneous groups. Also, we establish fractional logarithmic Gagliardo–Nirenberg and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups. In addition, we show blow-up results for the fractional heat equation with logarithmic nonlinearity on homogeneous groups.

Original languageEnglish
Article number7
JournalNonlinear Differential Equations and Applications
Volume27
Issue number1
DOIs
Publication statusPublished - Feb 1 2020

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Keywords

  • Blow-up
  • Fractional logarithmic Caffarelli–Kohn–Nirenberg inequality
  • Fractional logarithmic Gagliardo–Nirenberg inequality
  • Fractional logarithmic Sobolev inequality
  • Homogeneous group

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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