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 |
|---|---|
| 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 |
