Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Reproving Friedlander’s inequality with the de Rham complex

Fries, Magnus LU orcid ; Goffeng, Magnus LU orcid and Miranda, Germán LU orcid (2025) In Journal of Spectral Theory 15(4). p.1593-1613
Abstract

Inequalities between Dirichlet and Neumann eigenvalues of the Laplacian and of other differential operators have been intensively studied in the past decades. The aim of this paper is to introduce differential forms and the de Rham complex in the study of such inequalities. We show how differential forms lie hidden at the heart of the work of Rohleder on inequalities between Dirichlet and Neumann eigenvalues for the Laplacian on planar domains. Moreover, we extend the ideas of Rohleder to a new proof of Friedlander’s inequality for any bounded Lipschitz domain.

Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
de Rham complex, differential forms, Dirichlet Laplacian, eigenvalues inequalities, Friedlander’s inequality, Neumann Laplacian
in
Journal of Spectral Theory
volume
15
issue
4
pages
21 pages
publisher
European Mathematical Society Publishing House
external identifiers
  • scopus:105025665978
ISSN
1664-039X
DOI
10.4171/JST/582
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 European Mathematical Society.
id
388ac643-51c6-4cf7-aad3-30c8ea701bb7
date added to LUP
2026-02-16 17:07:43
date last changed
2026-02-16 17:08:29
@article{388ac643-51c6-4cf7-aad3-30c8ea701bb7,
  abstract     = {{<p>Inequalities between Dirichlet and Neumann eigenvalues of the Laplacian and of other differential operators have been intensively studied in the past decades. The aim of this paper is to introduce differential forms and the de Rham complex in the study of such inequalities. We show how differential forms lie hidden at the heart of the work of Rohleder on inequalities between Dirichlet and Neumann eigenvalues for the Laplacian on planar domains. Moreover, we extend the ideas of Rohleder to a new proof of Friedlander’s inequality for any bounded Lipschitz domain.</p>}},
  author       = {{Fries, Magnus and Goffeng, Magnus and Miranda, Germán}},
  issn         = {{1664-039X}},
  keywords     = {{de Rham complex; differential forms; Dirichlet Laplacian; eigenvalues inequalities; Friedlander’s inequality; Neumann Laplacian}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{4}},
  pages        = {{1593--1613}},
  publisher    = {{European Mathematical Society Publishing House}},
  series       = {{Journal of Spectral Theory}},
  title        = {{Reproving Friedlander’s inequality with the de Rham complex}},
  url          = {{http://dx.doi.org/10.4171/JST/582}},
  doi          = {{10.4171/JST/582}},
  volume       = {{15}},
  year         = {{2025}},
}