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.
-
Existence of multiple solutions to semilinear Dirichlet problem for subelliptic operator
Chen, Hua | Chen, Hong-Ge | Yuan, Xin-RuiSN Partial Differential Equations and Applications, Vol. 1 (2020), Iss. 6
https://doi.org/10.1007/s42985-020-00052-w [Citations: 3] -
Existence and multiplicity of solutions to Dirichlet problem for semilinear subelliptic equation with a free perturbation
Chen, Hua | Chen, Hong-Ge | Yuan, Xin-RuiJournal of Differential Equations, Vol. 341 (2022), Iss. P.504
https://doi.org/10.1016/j.jde.2022.09.021 [Citations: 4]