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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 weak and strong local minimizer $u\in{W^{1,2}(\Omega,\mathbb{R}^3)}$ 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 grows like $|{\rm det}Du|^q$ and 1<q<p<2, is $C^{1,\alpha}$ on an open subset $\Omega_0$ of Ω such that ${\it meas}(\Omega\setminus \Omega_0)=0$. Such functionals naturally arise from nonlinear elasticity problems. The key point in order to obtain the partial regularity result is to establish an energy estimate of Caccioppoli type, which is based on an appropriate choice of the test functions. The limit case $p=q\le 2$ is also treated for weak local minimizers.
- 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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