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 |
Published |
Elsevier Ltd
01.11.2017
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Subjects | |
Online Access | Get full text |
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Summary: | 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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ISSN: | 0252-9602 1572-9087 |
DOI: | 10.1016/S0252-9602(17)30098-X |