264 citations · 315 across the 5 of their papers we have counts for
5 papers
On the exponential decay of Laplacian eigenfunctions in planar domains with branches
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…
Geometrical structure of Laplacian eigenfunctions
Denis S. Grebenkov, Binh-Thanh Nguyen
We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the…
Localization of Laplacian eigenfunctions in circular, spherical and elliptical domains
Binh-Thanh Nguyen, Denis Grebenkov
We consider Laplacian eigenfunctions in circular, spherical and elliptical domains in order to discuss three kinds of high-frequency localization: whispering gallery modes, bouncin…
Trapped modes in finite quantum waveguides
Andrey L. Delitsyn, Binh-Thanh Nguyen, Denis S. Grebenkov
The Laplace operator in infinite quantum waveguides (e.g., a bent strip or a twisted tube) often has a point-like eigenvalue below the essential spectrum that corresponds to a trap…
Exponential decay of Laplacian eigenfunctions in domains with branches
Andrey Delitsyn, Binh-Thanh Nguyen, Denis S. Grebenkov
The behavior of Laplacian eigenfunctions in domains with branches is investigated. If an eigenvalue is below a threshold which is determined by the shape of the branch, the associa…