Lower bounds of Dirichlet eigenvalues for a class of finitely degenerate Grushin type elliptic operators

• Published in: Acta mathematica scientia Vol. 37; no. 6; pp. 1653 - 1664
• Main Authors: CHEN, Hua, CHEN, Hongge, DUAN, Yirui, HU, Xin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2017
• Subjects: 35J70; 35P15; Dirichlet eigenvalues; finitely degenerate elliptic operators; Grushin type operator; Hörmander's condition; sub-elliptic estimate; finitely degenerate elliptic operators; Hörmander's condition; Dirichlet eigenvalues; 35P15; 35J70; sub-elliptic estimate; Grushin type operator

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...