Interface boundary conditions of superconductor

Are the usual interface conditions for electromagnetic fields, i.e.
$$mathbf{n}_{12}times(mathbf{E}_1-mathbf{E}_2) = 0,$$
$$mathbf{n}_{12}bullet(mathbf{D}_1-mathbf{D}_2) = sigma_s,$$
$$mathbf{n}_{12}bullet(mathbf{B}_1-mathbf{B}_2) = 0,$$
$$mathbf{n}_{12}times(mathbf{H}_1-mathbf{H}_2) = mathbf{J}_s, $$
valid at the interface if one of the media is a superconductor? I would assume that they are since they are derived from Maxwell’s equations. Is this correct?