Abstract:
We study the eigenpairs of the Dirichlet Laplacian for plane waveguides with
corners. We prove that in presence of a non-trivial corner there exist
eigenvalues under the essential spectrum. Moreover we provide accurate
asymptotics for eigenpairs associated with the lowest eigenvalues in the
small angle limit. For this, we also investigate the eigenpairs of a
one-dimensional toy model related to the Born-Oppenheimer approximation, and
of the Dirichlet Laplacian on triangles with sharp angles. This is joint
work with Monique Dauge.
