File(s) not publicly available
Generalised twists, SO(n) and the p-energy over a space of measure preserving maps
journal contribution
posted on 2023-06-08, 00:42 authored by M S Shahrokhi-Dehkordi, Ali TaheriAli TaheriLet View the MathML source be a bounded Lipschitz domain and consider the energy functional View the MathML source with pset membership, variant]1,8[ over the space of measure preserving maps View the MathML source In this paper we introduce a class of maps referred to as generalised twists and examine them in connection with the Euler¿Lagrange equations associated with View the MathML source over View the MathML source. The main result is a surprising discrepancy between even and odd dimensions. Here we show that in even dimensions the latter system of equations admit infinitely many smooth solutions, modulo isometries, amongst such maps. In odd dimensions this number reduces to one. The result relies on a careful analysis of the full versus the restricted Euler¿Lagrange equations where a key ingredient is a necessary and sufficient condition for an associated vector field to be a gradient.
History
Publication status
- Published
Journal
Annales de l'Institut Henri Poincaré C, Analyse Non LinéaireISSN
0294-1449Publisher
ElsevierExternal DOI
Issue
5Volume
26Page range
1897-1924Pages
28.0Department affiliated with
- Mathematics Publications
Notes
EQUATIONS LOST IN ABSTRACTFull text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC