Singular subelliptic equations and Sobolev inequalities on Carnot groups

Prashanta Garain, Alexander Ukhlov

Research output: Contribution to journalArticlepeer-review

Abstract

In this article we study singular subelliptic p-Laplace equations and best constants in Sobolev inequalities on Carnot groups. We prove solvability of these subelliptic p-Laplace equations and existence of the minimizer of the corresponding variational problem. It leads to existence of the best constant in the corresponding (q, p)-Sobolev inequality, 0 < q< 1 , 1 < p< ν.

Original languageEnglish
Article number67
JournalAnalysis and Mathematical Physics
Volume12
Issue number2
DOIs
StatePublished - 1 Apr 2022

Keywords

  • Carnot groups
  • Singular problem
  • Sobolev inequality
  • Subelliptic operators

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics

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