Generalised twists, SO(n) and the p-energy over a space of measure preserving maps

Shahrokhi-Dehkordi, M S and Taheri, A (2009) Generalised twists, SO(n) and the p-energy over a space of measure preserving maps. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 26 (5). pp. 1897-1924. ISSN 0294-1449

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Abstract

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.

Item Type: Article
Additional Information: EQUATIONS LOST IN ABSTRACT
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Mohammad Shahrokhi-Dehkordi
Date Deposited: 06 Feb 2012 19:57
Last Modified: 08 Jun 2012 09:13
URI: http://sro.sussex.ac.uk/id/eprint/23204
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