3 papers
math.SP2025
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…
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…
math.SP2025
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…