A remark on the order of mixed Dirichlet-Neumann eigenvalues of polygons
Spectral Theory
2017-10-03 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
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 lowest eigenvalue to dominate the lowest eigenvalue of the Laplacian with the complementary boundary conditions (i.e. with Dirichlet replaced by Neumann and vice versa). The application of this result to triangles gives an affirmative partial answer to a recent conjecture. Moreover, we prove a further observation of similar flavor for right triangles.
Keywords
Cite
@article{arxiv.1710.00375,
title = {A remark on the order of mixed Dirichlet-Neumann eigenvalues of polygons},
author = {Jonathan Rohleder},
journal= {arXiv preprint arXiv:1710.00375},
year = {2017}
}