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# Eigenfunction Decay For the Neumann Laplacian on Horn-Like Domains

Published:2000-03-01
Printed: Mar 2000
• Julian Edward
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## Abstract

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: Neumann Laplacian, horn-like domain, spectrum
 MSC Classifications: 35P25 - Scattering theory [See also 47A40] 58G25 - unknown classification 58G25