LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS

doi:10.1016/S0252-9602(17)30098-X

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (6): 1653-1664.doi: 10.1016/S0252-9602(17)30098-X

LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS

陈化¹, 陈洪葛², 段忆苪², 胡鑫²

1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2016-08-31 修回日期:2017-03-14 出版日期:2017-12-25 发布日期:2017-12-25
作者简介:Hua CHEN,chenhua@whu.edu.cn;Hongge CHEN,hongge_chen@whu.edu.cn;Yirui DUAN,zzuduanyirui@163.com;Xin HU,hux@whu.edu.cn
基金资助:
This work is partially supported by the NSFC (11631011, 11626251).

LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS

Hua CHEN¹, Hongge CHEN², Yirui DUAN², Xin HU²

1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2016-08-31 Revised:2017-03-14 Online:2017-12-25 Published:2017-12-25
Supported by:
This work is partially supported by the NSFC (11631011, 11626251).

摘要/Abstract

摘要：

Let Ω be a bounded open domain in Rⁿ with smooth boundary ∂Ω, X=(X₁, X₂, …, X_m) be a system of real smooth vector fields defined on Ω and the boundary ∂Ω is non-characteristic for X. If X satisfies the Hörmander's condition, then the vector field is finitely degenerate and the sum of square operator △X=???20170608???X_j² is a finitely degenerate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △_X on Ω.

关键词: Dirichlet eigenvalues, finitely degenerate elliptic operators, Hörmander's condition, sub-elliptic estimate, Grushin type operator

Abstract:

Key words: Dirichlet eigenvalues, finitely degenerate elliptic operators, Hörmander's condition, sub-elliptic estimate, Grushin type operator

陈化, 陈洪葛, 段忆苪, 胡鑫. LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS[J]. 数学物理学报(英文版), 2017, 37(6): 1653-1664.

Hua CHEN, Hongge CHEN, Yirui DUAN, Xin HU. LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS[J]. Acta mathematica scientia,Series B, 2017, 37(6): 1653-1664.

参考文献

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LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS

LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS

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