English

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 pp-Laplacian and apply it to a parametrized perturbation by edge cuts. We show that the eigenvalues of the signed pp-Laplacian can be characterized as citical values of the parameter-dependent eigenvalues of a simpler graph.

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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}
}