Singular subelliptic equations and Sobolev inequalities on Carnot groups

Prashanta Garain, Alexander Ukhlov

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
Article number67
JournalAnalysis and Mathematical Physics
Issue number2
StatePublished - 1 Apr 2022


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

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics


Dive into the research topics of 'Singular subelliptic equations and Sobolev inequalities on Carnot groups'. Together they form a unique fingerprint.

Cite this