5 papers
Quantum trees which maximize higher eigenvalues are unbalanced
Jonathan Rohleder
The isoperimetric problem of maximizing all eigenvalues of the Laplacian on a metric tree graph within the class of trees of a given average edge length is studied. It turns out th…
Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains
Jussi Behrndt, Jonathan Rohleder
For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energi…
Inequalities between Neumann and Dirichlet eigenvalues of Schrödinger operators
Jonathan Rohleder
Given a Schrödinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann a…
Laplacians on bipartite metric graphs
Pavel Kurasov, Jonathan Rohleder
We study spectral properties of the standard (also called Kirchhoff) Laplacian and the anti-standard (or anti-Kirchhoff) Laplacian on a finite, compact metric graph. We show that t…
A remark on the order of mixed Dirichlet-Neumann eigenvalues of polygons
Jonathan Rohleder
Given the Laplacian on a planar, convex domain with piecewise linear boundary subject to mixed Dirichlet-Neumann boundary conditions, we provide a sufficient condition for its lowe…