Geodesic
Eigenfunction Decay For the Neumann Laplacian on Horn-Like Domains
Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 51-59

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DOI

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.
DOI : 10.4153/CMB-2000-007-4
Mots-clés : 35P25, 58G25, Neumann Laplacian, horn-like domain, spectrum 
Edward, Julian. Eigenfunction Decay For the Neumann Laplacian on Horn-Like Domains. Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 51-59. doi: 10.4153/CMB-2000-007-4
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     title = {Eigenfunction {Decay} {For} the {Neumann} {Laplacian} on {Horn-Like} {Domains}},
     journal = {Canadian mathematical bulletin},
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     year = {2000},
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     doi = {10.4153/CMB-2000-007-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-007-4/}
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