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.
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