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Eigenfunction Decay For the Neumann Laplacian on Horn-Like Domains

Published online by Cambridge University Press:  20 November 2018

Julian Edward
Julian Edward*
Affiliation:
Department of Mathematics Florida International University Miami, Florida 33199 U.S.A., e-mail: edwardj@fiu.edu
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Abstract

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The growth properties at infinity for eigenfunctions corresponding to embedded eigenvalues of the Neumann Laplacian on horn-like domains are studied. For domains that pinch at polynomial rate, it is shown that the eigenfunctions vanish at infinity faster than the reciprocal of any polynomial. For a class of domains that pinch at an exponential rate, weaker, ${{L}^{2}}$ bounds are proven. A corollary is that eigenvalues can accumulate only at zero or infinity.

Keywords

35P2558G25Neumann Laplacianhorn-like domainspectrum
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 1 , 01 March 2000 , pp. 51 - 59
Copyright
Copyright © Canadian Mathematical Society 2000

References

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