Spectral inequalities for magnetic Neumann Laplacian on rectangles

Tuyen Vu

Spectral inequalities for magnetic Neumann Laplacian on rectangles

Spectral Theory 2026-08-04 v1 Analysis of PDEs

Authors: Tuyen Vu

Abstract

We consider the magnetic Neumann Laplacian on rectangles, subject to non-homogeneous fields. We prove that the square is a local minimiser of the lowest eigenvalue among all rectangles of a fixed area for weak magnetic fields . We conjecture that it is a global minimiser both under the area or perimeter constraints and partially prove the conjecture by establishing lower and upper bounds to the principal eigenvalue.

Keywords

magnetic Neumann Laplacian rectangles spectral inequalities eigenvalue local minimiser global minimiser

Cite

@article{arxiv.2608.03843,
  title  = {Spectral inequalities for magnetic Neumann Laplacian on rectangles},
  author = {Tuyen Vu},
  journal= {arXiv preprint arXiv:2608.03843},
  year   = {2026}
}