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Lower Bounds of Dirichlet Eigenvalues for General Grushin Type Bi-Subelliptic Operators

Year:    2019

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 1 : pp. 66–84

Abstract

Let Ω be a bounded open domain in Rn with smooth boundary Ω. Let X=(X1,X2,,Xm) be a system of general Grushin type vector fields defined on Ω and the boundary Ω is non-characteristic for X. For ΔX=mj=1X2j, we denote λk as the k-th eigenvalue for the bi-subelliptic operator Δ2X on Ω. In this paper, by using the sharp sub-elliptic estimates and maximally hypoelliptic estimates, we give the optimal lower bound estimates of λk for the operator Δ2X.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-0002

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 1 : pp. 66–84

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Eigenvalues degenerate elliptic operators sub-elliptic estimate maximally hypoelliptic estimate bi-subelliptic operator.

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