Lower bounds of Dirichlet eigenvalues for a class of finitely degenerate Grushin type elliptic operators
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 oper...
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| Published in | Acta mathematica scientia Vol. 37; no. 6; pp. 1653 - 1664 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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01.11.2017
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| 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 ΔX=∑j=1mXj2 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 ΔX on Ω. |
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| AbstractList | 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 ΔX=∑j=1mXj2 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 ΔX on Ω. |
| Author | CHEN, Hua HU, Xin CHEN, Hongge DUAN, Yirui |
| Author_xml | – sequence: 1 givenname: Hua surname: CHEN fullname: CHEN, Hua email: chenhua@whu.edu.cn organization: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China – sequence: 2 givenname: Hongge surname: CHEN fullname: CHEN, Hongge email: hongge_chen@whu.edu.cn organization: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China – sequence: 3 givenname: Yirui surname: DUAN fullname: DUAN, Yirui email: zzuduanyirui@163.com organization: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China – sequence: 4 givenname: Xin surname: HU fullname: HU, Xin email: hux@whu.edu.cn organization: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| Cites_doi | 10.1007/BF01456804 10.1007/s00208-006-0030-x 10.1006/jfan.1994.1146 10.1016/j.jde.2013.04.004 10.1016/j.jde.2017.02.018 10.1007/s00526-011-0399-6 10.1090/S0002-9939-02-06834-X 10.1002/cpa.3160450104 10.1112/plms/s3-11.1.419 10.1007/BF01213210 10.1007/s00526-015-0885-3 10.1007/s11425-014-4895-y 10.5802/jedp.145 |
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| Keywords | finitely degenerate elliptic operators Hörmander's condition Dirichlet eigenvalues 35P15 35J70 sub-elliptic estimate Grushin type operator |
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| Snippet | 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... |
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| SubjectTerms | 35J70 35P15 Dirichlet eigenvalues finitely degenerate elliptic operators Grushin type operator Hörmander's condition sub-elliptic estimate |
| Title | Lower bounds of Dirichlet eigenvalues for a class of finitely degenerate Grushin type elliptic operators |
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