5 papers
Isoperimetric inequalities for the lowest magnetic Steklov eigenvalue
Ayman Kachmar, Vladimir Lotoreichik
This paper studies the optimization of the lowest eigenvalue of the magnetic Steklov problem on planar domains. In the bounded domain setting and for magnetic fields of moderate st…
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…
Optimisation of the lowest Robin eigenvalue in exterior domains of the hyperbolic plane
Antonio Celentano, David Krejcirik, Vladimir Lotoreichik
We consider the Robin Laplacian in the exterior of a bounded simply-connected Lipschitz domain in the hyperbolic plane. We show that the essential spectrum of this operator is $[\f…
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…