The de Rham Cohomology through Hilbert Space Methods
- We discuss canonical representations of the de Rham cohomology on a compact manifold with boundary. They are obtained by minimising the energy integral in a Hilbert space of differential forms that belong along with the exterior derivative to the domain of the adjoint operator. The corresponding Euler-Lagrange equations reduce to an elliptic boundary value problem on the manifold, which is usually referred to as the Neumann problem after Spencer.
Author details: | Ihsane Malass, Nikolai Nikolaevich TarkhanovORCiDGND |
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DOI: | https://doi.org/10.17516/1997-1397-2019-12-4-455-465 |
ISSN: | 1997-1397 |
ISSN: | 2313-6022 |
Title of parent work (English): | Journal of Siberian Federal University. Mathematics & physics |
Publisher: | Sibirskij Federalʹnyj Universitet |
Place of publishing: | Krasnoyarsk |
Publication type: | Article |
Language: | English |
Date of first publication: | 2019/12/01 |
Publication year: | 2019 |
Release date: | 2021/05/05 |
Tag: | De Rham complex; Hodge theory; Neumann problem; cohomology |
Volume: | 12 |
Issue: | 4 |
Number of pages: | 11 |
First page: | 455 |
Last Page: | 465 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Bronze Open-Access |