24 citations · 77 across the 23 of their papers we have counts for
33 papers
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 first eigenvalue and eigenfunction of the Laplacian with mixed boundary conditions
Nausica Aldeghi, Jonathan Rohleder
We consider the eigenvalue problem for the Laplacian with mixed Dirichlet and Neumann boundary conditions. For a certain class of bounded, simply connected planar domains we prove…
Inequalities between Neumann and Dirichlet Laplacian eigenvalues on planar domains
Jonathan Rohleder
We generalize a classical inequality between the eigenvalues of the Laplacians with Neumann and Dirichlet boundary conditions on bounded, planar domains: in 1955, Payne proved that…
Estimates for the lowest Neumann eigenvalues of parallelograms and domains of constant width
Corentin Léna, Jonathan Rohleder
We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This…
Spectral Theory for Schrödinger operators on compact metric graphs with and couplings: a survey
Jonathan Rohleder, Christian Seifert
Spectral properties of Schrödinger operators on compact metric graphs are studied and special emphasis is put on differences in the spectral behavior between different classes of v…
Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions
Nausica Aldeghi, Jonathan Rohleder
The eigenvalue problem for the Laplacian on bounded, planar, convex domains with mixed boundary conditions is considered, where a Dirichlet boundary condition is imposed on a part…