6 papers · 1 filter
Comparison inequalities for Dirichlet-to-Neumann maps
Denis S. Grebenkov, Michael Levitin, Karl-Mikael Perfekt +1
We prove comparison inequalities for Dirichlet-to-Neumann maps corresponding to different non-positive Helmholtz parameters. For convex domains our bounds are sharp, and the result…
Pólya's conjecture for higher-dimensional Neumann balls
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
We prove Pólya's conjecture for the Neumann eigenvalues of the Laplacian on Euclidean balls in dimensions three and higher. The proof further develops the approach introduced in o…
The exterior Steklov problem for Euclidean domains
Lukas Bundrock, Alexandre Girouard, Denis S. Grebenkov +2
We investigate the Steklov eigenvalue problem in an exterior Euclidean domain. First, we present several formulations of this problem and establish the equivalences between them. N…
Spectral properties of the Dirichlet-to-Neumann map for the Helmholtz equation
Denis S. Grebenkov, Michael Levitin, Iosif Polterovich
The study of the Dirichlet-to-Neumann map and the associated Steklov problem for the Laplace equation has been a central topic in spectral geometry over the past decade. In this su…
Pólya's conjecture for Dirichlet eigenvalues of annuli
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks a…
Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues
Michael Levitin, Leonid Parnovski, Iosif Polterovich +1
In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is on the two-dimensional…