Journal article
Complexes from complexes
- Abstract:
- This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a systematic procedure which, starting from well-understood differential complexes such as the de Rham complex, derives new complexes and deduces the properties of the new complexes from the old. We relate the cohomology of the output complex to that of the input complexes and show that the new complex has closed ranges, and, consequently, satisfies a Hodge decomposition, Poincaré-type inequalities, well-posed Hodge–Laplacian boundary value problems, regular decomposition, and compactness properties on general Lipschitz domains.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
-
-
(Preview, Accepted manuscript, pdf, 340.0KB, Terms of use)
-
- Publisher copy:
- 10.1007/s10208-021-09498-9
Authors
+ U.S. National Science Foundation
More from this funder
- Funder identifier:
- https://ror.org/021nxhr62
- Grant:
- DMS-1719694
- Publisher:
- Springer
- Journal:
- Foundations of Computational Mathematics More from this journal
- Volume:
- 21
- Issue:
- 6
- Pages:
- 1739-1774
- Publication date:
- 2021-03-05
- Acceptance date:
- 2021-01-12
- DOI:
- EISSN:
-
1615-3383
- ISSN:
-
1615-3375
- Language:
-
English
- Keywords:
- Pubs id:
-
2282285
- Local pid:
-
pubs:2282285
- Source identifiers:
-
W3032617580
- Deposit date:
-
2026-08-10
- ARK identifier:
Terms of use
- Copyright holder:
- SFoCM
- Copyright date:
- 2021
- Rights statement:
- © SFoCM 2021
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Springer at https://dx.doi.org/10.1007/s10208-021-09498-9
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