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1. CMB 2000 (vol 43 pp. 51)

Edward, Julian
Eigenfunction Decay For the Neumann Laplacian on Horn-Like Domains
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
Categories:35P25, 58G25

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