Spectral flow for pair compatible equipartitions
(2022) In Communications in Partial Differential Equations 47(1). p.169-196- Abstract
We show that a recent spectral flow approach proposed by Berkolaiko–Cox–Marzuola for analyzing the nodal deficiency of the nodal partition associated to an eigenfunction can be extended to more general partitions. To be more precise, we work with spectral equipartitions that satisfy a pair compatible condition. Nodal partitions and spectral minimal partitions are examples of such partitions. Along the way, we discuss different approaches to the Dirichlet-to-Neumann operators: via Aharonov–Bohm operators, via a double covering argument, and via a slitting of the domain.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/efaf1d41-eafa-4f93-a5e4-5bf2a37443ce
- author
- Helffer, Bernard and Sundqvist, Mikael Persson LU
- organization
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Aharonov–Bohm Hamiltonians, Dirichlet-to-Neumann operators, nodal deficiency, Spectral flow
- in
- Communications in Partial Differential Equations
- volume
- 47
- issue
- 1
- pages
- 169 - 196
- publisher
- Taylor & Francis
- external identifiers
-
- scopus:85112621116
- ISSN
- 0360-5302
- DOI
- 10.1080/03605302.2021.1955257
- language
- English
- LU publication?
- yes
- id
- efaf1d41-eafa-4f93-a5e4-5bf2a37443ce
- date added to LUP
- 2021-09-10 09:45:58
- date last changed
- 2022-06-29 19:01:13
@article{efaf1d41-eafa-4f93-a5e4-5bf2a37443ce,
abstract = {{<p>We show that a recent spectral flow approach proposed by Berkolaiko–Cox–Marzuola for analyzing the nodal deficiency of the nodal partition associated to an eigenfunction can be extended to more general partitions. To be more precise, we work with spectral equipartitions that satisfy a pair compatible condition. Nodal partitions and spectral minimal partitions are examples of such partitions. Along the way, we discuss different approaches to the Dirichlet-to-Neumann operators: via Aharonov–Bohm operators, via a double covering argument, and via a slitting of the domain.</p>}},
author = {{Helffer, Bernard and Sundqvist, Mikael Persson}},
issn = {{0360-5302}},
keywords = {{Aharonov–Bohm Hamiltonians; Dirichlet-to-Neumann operators; nodal deficiency; Spectral flow}},
language = {{eng}},
number = {{1}},
pages = {{169--196}},
publisher = {{Taylor & Francis}},
series = {{Communications in Partial Differential Equations}},
title = {{Spectral flow for pair compatible equipartitions}},
url = {{http://dx.doi.org/10.1080/03605302.2021.1955257}},
doi = {{10.1080/03605302.2021.1955257}},
volume = {{47}},
year = {{2022}},
}