  Korn's inequality plays an important role in linear elasticity theory. This
inequality bounds the norm of the derivatives of the displacement vector by the
norm of the linearized strain tensor. The kernel of the linearized strain
tensor are the infinitesimal rigid-body translations and rotations (Killing
vectors). We generalize this inequality by replacing the linearized strain
tensor by its trace free part. That is, we obtain a stronger inequality in
which the kernel of the relevant operator are the conformal Killing vectors.
The new inequality has applications in General Relativity.
