Eigenfunction decay for the Neumann Laplacian on horn-like domains Article

cited authors

  • Edward, J

fiu authors

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, L2 bounds are proven. A corollary is that eigenvalues can accumulate only at zero or infinity.

publication date

  • January 1, 2000

Digital Object Identifier (DOI)

start page

  • 51

end page

  • 59

volume

  • 43

issue

  • 1