6 papers · 1 filter
Convergence of Schrödinger operators on domains with scaled resonant potentials
Vladimir Lotoreichik, Olaf Post
We consider Schrödinger operators on a bounded, smooth domain of dimension with Dirichlet boundary conditions and a properly scaled potential, which depends only on the…
On shape optimization with large magnetic fields in two dimensions
Vladimir Lotoreichik, Léo Morin
This paper aims to show that, in the limit of strong magnetic fields, the optimal domains for eigenvalues of magnetic Laplacians tend to exhibit symmetry. We establish several asym…
A note on optimization of the second positive Neumann eigenvalue for parallelograms
Vladimir Lotoreichik, Jonathan Rohleder
It has recently been conjectured by Bogosel, Henrot, and Michetti that the second positive eigenvalue of the Neumann Laplacian is maximized, among all planar convex domains of fixe…
On the Laplace operator with a weak magnetic field in exterior domains
Ayman Kachmar, Vladimir Lotoreichik, Mikael Sundqvist
We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate…
Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian
Vladimir Lotoreichik
We consider the magnetic Laplacian with the homogeneous magnetic field in two and three dimensions. We prove that the -th magnetic Neumann eigenvalue of a bounded convex pla…
Quasi-conical domains with embedded eigenvalues
David Krejcirik, Vladimir Lotoreichik
The spectrum of the Dirichlet Laplacian on any quasi-conical open set coincides with the non-negative semi-axis. We show that there is a connected quasi-conical open set such that…