Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Spectral Theory

arXiv:2202.01001 (math)
[Submitted on 2 Feb 2022 (v1), last revised 20 Sep 2022 (this version, v3)]

Title:Non-monotonicity for the 3D magnetic Robin Laplacian

Authors:Germán Miranda
View PDF
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 $+\infty$.
Comments: 7 pages, 1 figure
Subjects: Spectral Theory (math.SP)
MSC classes: 35P05
Cite as: arXiv:2202.01001 [math.SP]
  (or arXiv:2202.01001v3 [math.SP] for this version)
  https://doi.org/10.48550/arXiv.2202.01001

Submission history

From: Germán Miranda [view email]
[v1] Wed, 2 Feb 2022 12:39:21 UTC (27 KB)
[v2] Fri, 8 Jul 2022 13:37:10 UTC (27 KB)
[v3] Tue, 20 Sep 2022 09:31:27 UTC (78 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.SP
< prev   |   next >
new | recent | 2022-02
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)