1303.0051 (Binh T. Nguyen et al.)

On the exponential decay of Laplacian eigenfunctions in planar domains
with branches    [PDF]

Binh T. Nguyen, Andrey L. Delytsin, Denis S. Grebenkov

We consider the eigenvalue problem for the Laplace operator in a planar domain which can be decomposed into a bounded domain of arbitrary shape and elongated \branches" of variable cross-sectional pro?les. When the eigenvalue is smaller than a prescribed threshold, the corresponding eigenfunction decays exponentially along each branch. We prove this behavior for Robin boundary condition and illustrate some related results by numerically computed eigenfunctions.

View original: http://arxiv.org/abs/1303.0051