Inequalities of Dirichlet eigenvalues for degenerate elliptic partial differential operators

الأصل · EN

Let Xⱼ,Yⱼ(j = 1, · · ·,n) be vector fields satisfying Hörmander's condition and Δₗ = ∑ⱼ ₌ ₁ⁿ (Xⱼ² + Yⱼ²). In this paper, we establish some inequalities of Dirichlet eigenvalues for degenerate elliptic partial differential operator Δₗ and Δₗ². These inequalities extend Yang's inequalities for Dirichlet eigenvalues of Laplacian to the settings here and the forms of inequalities are more general than Yang's inequalities. To obtain them, we give a generalization of the inequality by Chebyshev.