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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 Taheri
Let 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 Linéaire

ISSN

0294-1449

Publisher

Elsevier

Issue

5

Volume

26

Page range

1897-1924

Pages

28.0

Department affiliated with

  • Mathematics Publications

Notes

EQUATIONS LOST IN ABSTRACT

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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