= Energy uniqueness for traction-driven elasticity
{title2=$E=\tfrac12\int(\rho|\dot{\mathbf w}|^2+c_{ijpq}e_{ij}e_{pq})\,dV$}
The difference of two solutions with the same <body force>, boundary <traction> and initial data satisfies a homogeneous elastic equation with zero boundary <work>. Multiplication by its <velocity> and <integration by parts> conserve the displayed positive <energy>. Zero initial <energy> forces zero <velocity> for all times, and zero initial <displacement field> then forces zero <displacement field>. Rigid zero-strain motions do not cause nonuniqueness after initial data are fixed. This assumes positive <mass density>, stable real elastic moduli and sufficient regularity for the <energy> identity.
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