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- Title
Estimates of Dirichlet eigenvalues for degenerate ▵μ-Laplace operator.
- Authors
Chen, Hua; Chen, Hong-Ge; Li, Jin-Ning
- Abstract
Let Ω be a bounded open domain in R n and ▵ μ = ∑ j = 1 n ∂ x j (μ j 2 (x) ∂ x j) be a class of degenerate elliptic operator with continuous nonnegative coefficients μ 1 , μ 2 , ... , μ n . Denote by λ k the kth Dirichlet eigenvalue of the self-adjoint degenerate elliptic operator - ▵ μ on Ω . If the coefficients μ 1 , μ 2 , ... , μ n satisfy some general assumptions, we give an explicit lower bound estimate of λ k . Moreover, if the coefficients μ 1 ... , μ n are homogeneous functions with respect to a group of dilation, then we obtain an explicit sharp lower bound estimate for λ k , which has a polynomially growth in k of the order related to the homogeneous dimension. Finally, we also establish an upper bound estimate of λ k for general self-adjoint degenerate elliptic operator ▵ μ .
- Subjects
ESTIMATES; EIGENVALUES; DEGENERATE differential equations; ELLIPTIC operators
- Publication
Calculus of Variations & Partial Differential Equations, 2020, Vol 59, Issue 4, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-020-01765-x