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

被引：0

作者：

Suragan, Durvudkhan ^{[1
]}

Yessirkegenov, Nurgissa ^{[2
]}

机构：

[1] Nazarbayev Univ, Dept Math, Astana, Kazakhstan

[2] Suleyman Demirel Univ, Kaskelen, Kazakhstan

来源：

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2023年 / 16卷 / 03期

关键词：

Poincare inequalitiy; Baouendi-Grushin operator; eigenfunction; blow-up solution; HARDY INEQUALITIES; BLOW-UP; EQUATIONS; NONEXISTENCE; THEOREMS; OPERATOR;

D O I：

10.1142/S1793557123500419

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

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页数：8

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