English

A note on domain monotonicity for the Neumann eigenvalues of the Laplacian

Metric Geometry 2023-09-11 v5 Analysis of PDEs Functional Analysis Spectral Theory

Abstract

Given a convex domain and its convex sub-domain we prove a variant of domain monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our method we also obtain an upper bound for Neumann eigenvalues of the Laplacian of a convex domain.

Keywords

Cite

@article{arxiv.2202.03598,
  title  = {A note on domain monotonicity for the Neumann eigenvalues of the Laplacian},
  author = {Kei Funano},
  journal= {arXiv preprint arXiv:2202.03598},
  year   = {2023}
}

Comments

Final version. To appear in Illinois J. Math