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On one-homogeneous solutions to elliptic systems with spatial variable dependence in two dimensions

Bevan, JJ (2010) On one-homogeneous solutions to elliptic systems with spatial variable dependence in two dimensions P ROY SOC EDINB A, 140. pp. 449-475.

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Abstract

We extend a result from Phillips by showing that one-homogeneous solutions of certain elliptic systems in divergence form either do not exist; or must be affine. The result is novel in two ways. Firstly, the system is allowed to depend (in a sufficiently smooth way) on the spatial variable x. Secondly, Phillips's original result is shown to apply to W-1,W-2 one-homogeneous solutions, from which his treatment of Lipschitz solutions follows as a special case. A singular one-homogeneous solution to an elliptic system violating the hypotheses of the main theorem is constructed using a variational method.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Bevan, JJUNSPECIFIEDUNSPECIFIED
Date : March 2010
Identification Number : 10.1017/S0308210508000516
Uncontrolled Keywords : NONLINEAR ELASTICITY, POLYCONVEX FUNCTIONALS, MAXIMAL SMOOTHNESS, MINIMIZERS, REGULARITY, EQUATIONS
Additional Information : Copyright 2010 The Royal Society of Edinburgh
Depositing User : Symplectic Elements
Date Deposited : 30 Oct 2015 09:17
Last Modified : 30 Oct 2015 09:18
URI: http://epubs.surrey.ac.uk/id/eprint/809154

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