Inequalities between Neumann and Dirichlet eigenvalues of Schr\"odinger operators
Spectral Theory
2020-03-17 v3 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
Given a Schr\"odinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann and Dirichlet boundary conditions, respectively. The obtained inequalities depend partially on monotonicity and convexity properties of the potential. The results are counterparts of classical inequalities for the Laplacian but display some distinction between the one-dimensional case and higher dimensions.
Keywords
Cite
@article{arxiv.1907.02316,
title = {Inequalities between Neumann and Dirichlet eigenvalues of Schr\"odinger operators},
author = {Jonathan Rohleder},
journal= {arXiv preprint arXiv:1907.02316},
year = {2020}
}