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Model problems from nonlinear elasticity:partial regularity results
Published online by Cambridge University Press: 14 February 2007
Abstract
In this paper we prove that every weakand strong localminimizer $u\in{W^{1,2}(\Omega,\mathbb{R}^3)}$ 
of the functional $I(u)=\int_\Omega|Du|^2+f({\rm Adj}Du)+g({\rm det}Du),$ 
where $ u:\Omega\subset\mathbb{R}^3\to \mathbb{R}^3$ 
, f grows like $|{\rm Adj}Du|^p$ 
, g growslike $|{\rm det}Du|^q$ 
and1<q<p<2, is $C^{1,\alpha}$ 
on an opensubset $\Omega_0$ 
of Ω such that ${\it meas}(\Omega\setminus \Omega_0)=0$ 
. Suchfunctionals naturally arise from nonlinear elasticity problems. The keypoint in order to obtain the partial regularity result is toestablish an energy estimate of Caccioppoli type, which is based onan appropriate choice of the test functions. The limit case $p=q\le 2$ 
is also treated for weak local minimizers.
Information
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 1 , January 2007 , pp. 120 - 134
- Copyright
- © EDP Sciences, SMAI, 2007
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