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

Durvudkhan Suragan; Nurgissa Yessirkegenov

doi:10.1142/S1793557123500419

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

Durvudkhan Suragan, Nurgissa Yessirkegenov

Research output: Contribution to journal › Article › peer-review

Abstract

In this note, we establish a sharp remainder formula for the Poincaré inequality for the Baouendi-Grushin 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.

Original language	English
Article number	2350041
Journal	Asian-European Journal of Mathematics
DOIs	https://doi.org/10.1142/S1793557123500419
Publication status	Accepted/In press - 2022

Keywords

Baouendi-Grushin operator
blow-up solution
eigenfunction
Poincaré inequalitiy

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1142/S1793557123500419

Cite this

@article{c247e8c9af0c488297a29408e396ca55,

title = "Sharp remainder of the Poincar{\'e} inequality for Baouendi-Grushin vector fields",

abstract = "In this note, we establish a sharp remainder formula for the Poincar{\'e} inequality for the Baouendi-Grushin 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.",

keywords = "Baouendi-Grushin operator, blow-up solution, eigenfunction, Poincar{\'e} inequalitiy",

author = "Durvudkhan Suragan and Nurgissa Yessirkegenov",

note = "Publisher Copyright: {\textcopyright} 2023 World Scientific Publishing Company.",

year = "2022",

doi = "10.1142/S1793557123500419",

language = "English",

journal = "Asian-European Journal of Mathematics",

issn = "1793-5571",

publisher = "World Scientific Publishing Co. Pte Ltd",

}

TY - JOUR

T1 - Sharp remainder of the Poincaré inequality for Baouendi-Grushin vector fields

AU - Suragan, Durvudkhan

AU - Yessirkegenov, Nurgissa

PY - 2022

Y1 - 2022

N2 - In this note, we establish a sharp remainder formula for the Poincaré inequality for the Baouendi-Grushin 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.

AB - In this note, we establish a sharp remainder formula for the Poincaré inequality for the Baouendi-Grushin 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.

KW - Baouendi-Grushin operator

KW - blow-up solution

KW - eigenfunction

KW - Poincaré inequalitiy

UR - http://www.scopus.com/inward/record.url?scp=85135481243&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85135481243&partnerID=8YFLogxK

U2 - 10.1142/S1793557123500419

DO - 10.1142/S1793557123500419

M3 - Article

AN - SCOPUS:85135481243

SN - 1793-5571

JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

M1 - 2350041

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this