Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions
Spectral Theory
2023-01-26 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
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 of the boundary and a Neumann boundary condition on its complement. Given two different such choices of boundary conditions for the same domain, we prove inequalities between their lowest eigenvalues. As a special case, we prove parts of a conjecture on the order of mixed eigenvalues of triangles.
Cite
@article{arxiv.2212.05889,
title = {Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions},
author = {Nausica Aldeghi and Jonathan Rohleder},
journal= {arXiv preprint arXiv:2212.05889},
year = {2023}
}