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Enclosure Theorems for Eigenvalues of Elliptic Operators

Published online by Cambridge University Press:  20 November 2018

John C. Clements
John C. Clements*
Affiliation:
University of Washington, Seattle, Washington
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Let L be the linear, elliptic, self-adjoint partial differential operator given by

where Dj denotes partial differentiation with respect to xj, 1 ≤ j ≤ n, b is a positive, continuous real-valued function of x = (x1,…,xn) in n-dimensional Euclidean space En, the aij are real-valued functions possessing uniformly continuous first partial derivatives in En and the matrix {aij} is everywhere positive definite. A solution u of Lu = 0 is assumed to be of class C1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 1 - 7
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Courant, R., and Hilbert, D., Methods of Mathematical Physics, Vol. II, Interscience, New York, 1962.Google Scholar
2. Duff, G. F. D., Partial Differential Equations, Univ. of Toronto Press, 1956.Google Scholar
3. Mikhlin, S. G., The Problem of the Minimum of a Quadratic Functional, Holden-Day, San Francisco, 1965.Google Scholar
4. Swanson, C. A., Enclosure theorems for eigenvalues of elliptic operators, Proc. Am. Math. Soc. 17 (1966), 18-25.Google Scholar
5. Swanson, C. A., 'On spectral estimation', Bull. Am. Math. Soc. 68 (1962).Google Scholar