# The Upper Bounds of Arbitrary Eigenvalues for Uniformly Elliptic Operators with Higher Orders

The Upper Bounds of Arbitrary Eigenvalues for Uniformly Elliptic Operators with Higher Orders Let Ω ⊂ R m (m ≥ 2) be a bounded domain with piecewise smooth and Lipschitz boundary ∂Ω. Let t and r be two nonnegative integers with t ≥ r +1. In this paper, we consider the variable-coefficient eigenvalue problems with uniformly elliptic differential operators on the left-hand side and (−Δ) r on the right-hand side. Some upper bounds of the arbitrary eigenvalue are obtained, and several known results are generalized. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# The Upper Bounds of Arbitrary Eigenvalues for Uniformly Elliptic Operators with Higher Orders

, Volume 22 (4) – Jan 1, 2006
10 pages

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Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-006-0332-5
Publisher site
See Article on Publisher Site

### Abstract

Let Ω ⊂ R m (m ≥ 2) be a bounded domain with piecewise smooth and Lipschitz boundary ∂Ω. Let t and r be two nonnegative integers with t ≥ r +1. In this paper, we consider the variable-coefficient eigenvalue problems with uniformly elliptic differential operators on the left-hand side and (−Δ) r on the right-hand side. Some upper bounds of the arbitrary eigenvalue are obtained, and several known results are generalized.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2006

### References

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