For a bounded corner domain
,
we consider the attractive Robin Laplacian in
with
large Robin parameter. Exploiting multiscale analysis and a recursive procedure, we
have a precise description of the mechanism giving the bottom of the spectrum. It
allows also the study of the bottom of the essential spectrum on the associated
tangent structures given by cones. Then we obtain the asymptotic behavior
of the principal eigenvalue for this singular limit in any dimension, with
remainder estimates. The same method works for the Schrödinger operator in
with a strong
attractive
-interaction
supported on .
Applications to some Ehrling-type estimates and the analysis of the critical
temperature of some superconductors are also provided.
Keywords
Robin Laplacian, eigenvalues estimates, corner domains