Eigenvalues of the discrete p-Laplacian via graph surgery
Analysis of PDEs
2025-09-09 v1
Abstract
We develop a Hellmann--Feynman type perturbation theory for the discrete signed -Laplacian and apply it to a parametrized perturbation by edge cuts. We show that the eigenvalues of the signed -Laplacian can be characterized as citical values of the parameter-dependent eigenvalues of a simpler graph.
Keywords
Cite
@article{arxiv.2509.06686,
title = {Eigenvalues of the discrete p-Laplacian via graph surgery},
author = {Gregory Berkolaiko and Matthias Hofmann},
journal= {arXiv preprint arXiv:2509.06686},
year = {2025}
}