Asymptotic behaviour of eigenfunctions in a thin cylinder with distorted ends
Tiziana Durante · AIP conference proceedings · 2013
We consider a mixed boundary value problem for the Laplace operator in a straight cylinder with curved ends with the Dirichlet conditions on the lateral side. We prove that when the ratio between the diameter and the length of the cylinder tends to zero, the principal eigenfunction concentrates in the vicinity of the ends and decays exponentially in the interior.