# Euler-Lagrange Equation for a functional involving symmetric gradients

I struggle to compute the Euler-Lagrange equation for the following functional $\int_{\Omega} (\nabla^{s} u) D \nabla^{s} u \mathrm{d}\Omega$, where u is a vector valued function u = (u1 (x,y), u2 (x,y)), $[\nabla^{s}u]_{ij} = 1/2 (u_{i,j} + u_{j,i})$ and $D_{ijkl} = D_{jilk}$. I lack practice with such manipulations: when I try the explicit computation $\int_{\Omega} \frac{1}{2}(u_{i,j}+u_{j,i}) C_{ijkl}(u_{k,l}+u_{l,k})$ things spin out of control rather quickly... thanks

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If my question is not considered only because there is no trace in it of any solving effort, I would be glad to amend it, as there is plenty of effort being thrown at it, it is really important! thank you very much –  Buco Nov 11 '13 at 18:34