On the Galilean invariance of balance equation for a singular surface in continuum

The paper contains the derivation of the Galilean invariant form of the balance equations for a singular surface. It is proved that such an invariance requires a certain structure of the surface sources. We illustrate the formal results, applying them in the theory of capillarity, the theory of very strong shock waves and the theory of Mueller's material. In the last case, we derive an inequality, limiting the strength of non-adiabatic shock waves.