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Eigenfunction Decay For the Neumann Laplacian on Horn-Like Domains
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- Journal:
- Canadian Mathematical Bulletin / Volume 43 / Issue 1 / 01 March 2000
- Published online by Cambridge University Press:
- 20 November 2018, pp. 51-59
- Print publication:
- 01 March 2000
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- Article
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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.
