English

Non-monotonicity for the 3D magnetic Robin Laplacian

Spectral Theory 2022-09-21 v3

Abstract

Previous works provided several counterexamples to monotonicity of the lowest eigenvalue for the magnetic Laplacian in the two-dimensional case. However, the three-dimensional case is less studied. We use the results obtained by Helffer, Kachmar and Raymond to provide one of the first counterexamples in 3D. Considering the Robin magnetic Laplacian on the unit ball with a constant magnetic field, we show the non-monotonicity of the lowest eigenvalue asymptotics when the Robin parameter tends to ++\infty.

Keywords

Cite

@article{arxiv.2202.01001,
  title  = {Non-monotonicity for the 3D magnetic Robin Laplacian},
  author = {Germán Miranda},
  journal= {arXiv preprint arXiv:2202.01001},
  year   = {2022}
}

Comments

7 pages, 1 figure