Hostname: page-component-cb9f654ff-fg9bn Total loading time: 0 Render date: 2025-08-21T13:52:52.721Z Has data issue: false hasContentIssue false
  • English
  • Français

Domain Perturbations of the Biharmonic Operator

Published online by Cambridge University Press:  20 November 2018

C. A. Swanson
C. A. Swanson*
Affiliation:
The University of British Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Eigenvalue problems for the biharmonic operator (iterated Laplacian) L = ΔΔ will be studied on bounded plane domains. Our purpose is to obtain asymptotic variational formulae for eigenvalues and eigenfunctions under the deformation of removing an ∊-disk and adjoining additional boundary conditions on the new boundary component thereby introduced, valid on a positive interval 0 < ∊ < ∊0. Eigenvalue problems can be considered in connection with each of the following sets of homogeneous boundary conditions.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 1053 - 1063
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Bergman, Stefan, The kernel function and conformai mapping , Amer. Math. Soc, Mathematical Surveys No. V (New York, 1950).Google Scholar
2. Courant, R. and Hilbert, D., Methods of mathematical physics (New York, 1953).Google Scholar
3. D. Duff, G. F., Partial differential equations (Toronto, 1956).Google Scholar
4. Friedrichs, K., Die Randwert- und Eigenwertprobleme aus der Théorie der elastischen Flatten, Math. Ann., 98 (1928), 206–247.Google Scholar
5. Gárding, Lars, DirichleVs problem for linear elliptic partial differential equations. Math. Scand., 1 (1953), 55–72.Google Scholar
6. Gould, S. H., Variational methods for eigenvalue problems (Toronto, 1957).Google Scholar
7. Swanson, C. A., On spectral estimation, Bull. Amer. Math. Soc, 68 (1962), 33–35.Google Scholar
8. Swanson, C. A., Asymptotic variational formulae for eigenvalues, Can. Math. Bull., 6 (1963), 15–25.Google Scholar
9. Weinstock, R., Greeris functions for a fourth-order partial differential equation, Technical report 25, Contract N6ori-106 TASK ORDER 5 (NR-043-992) for Office of Naval Research (Stanford University, 1952).Google Scholar