 Elastic energy uniqueness with restoring boundary springs

For a time-independent symmetric negative semidefinite boundary matrix $k$, the difference of two linear elasticity solutions with the same data has traction $kw$. Integration by parts conserves the displayed nonnegative energy. Zero initial data force zero velocity and then zero displacement. The matrix $-k$ is the stiffness of boundary springs to a prescribed support; null directions are traction-free.