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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…
math.SP2025
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 d…
math.SP2025
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…