Articles

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

  • Hua CHEN ,
  • Hongge CHEN ,
  • Yirui DUAN ,
  • Xin HU
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  • 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 date: 2016-08-31

  Revised date: 2017-03-14

  Online published: 2017-12-25

Supported by

This work is partially supported by the NSFC (11631011, 11626251).

Abstract

Let Ω be a bounded open domain in Rn with smooth boundary Ω, X=(X1, X2, …, Xm) 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???Xj2 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.

Cite this article

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 . DOI: 10.1016/S0252-9602(17)30098-X

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