Sharp remainder of the Poincare inequality for Baouendi-Grushin vector fields

Suragan D., Yessirkegenov N.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.16, no.3, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.1142/s1793557123500419
  • Journal Name: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Poincare inequalitiy, Baouendi-Grushin operator, eigenfunction, blow-up solution, HARDY INEQUALITIES, BLOW-UP, EQUATIONS, NONEXISTENCE, THEOREMS, OPERATOR
  • Süleyman Demirel University Affiliated: No

Abstract

In this note, we establish a sharp remainder formula for the Poincare inequality for the Baouendi-Crushin vector fields. We give a simple proof for it without using the variational principle. As an application, we obtain a blow-up result for solutions to the Dirichlet initial-boundary value problem for the Baouendi-Grushin heat operator.