D. Berghaus

collaborators

2 papers

math.NA2022

Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry

David Berghaus, Robert Stephen Jones, Hartmut Monien +1

We numerically compute the lowest Laplacian eigenvalues of several two-dimensional shapes with dihedral symmetry at arbitrary precision arithmetic. Our approach is based on the met…

math.NT2021

On Dirichlet eigenvalues of regular polygons

David Berghaus, Bogdan Georgiev, Hartmut Monien +1

We prove that the first Dirichlet eigenvalue of a regular $N$ -gon of area $π$ has an asymptotic expansion of the form $λ_{1} (1 + \sum_{n \geq 3} C_{n} (λ_{1}) N^{- n})$ as $N \to \infty$ , where $λ_…