  We are concerned with the well-posedness of linear elliptic systems posed on
$\mathbb{R}^d$. The concrete problem of interest, for which we require this
theory, arises from the linearization of the equations of anisotropic finite
elasticity, however, our results are more generally applicable to
translation-invariant problem posed on $\mathbb{R}^d$. We describe a variant of
homogeneous Sobolev spaces, which are convenient for treating problems of this
kind.
