  Nonequilibrium dynamics at interfaces is generally driven by a chemical
potential. Here we demonstrate a generic technique to derive the basic
equations of motion, boundary conditions and the chemical potential in a
consistent way from fundamental variational principles. As a particular
example, we consider a solid surface with elastodynamic effects, together with
surface energy and tension. We apply the generic results to perform a linear
stability analysis of a planar front subjected to uniaxial stress
(Asaro-Tiller-Grinfeld instability), here also with surface tension.
