Geometrical conservation laws for Maxwell and elasticity systems (Q1861407)

The author gives a sharp form of geometrical conservation laws for the Maxwell system in terms of the distribution theory. It is shown that the conservation laws hold through any singular point of the wave front, in particular, that the residue of the energy flux of the electromagnetic field is preserved through an arbitrary caustic. This also implies Luneberg's result. The author obtains Rytov's geometric law in a sharp form, which is free of the above limitations. The elasticity system and Levin's and Rytov's geometric conservation law are also adapted to distribution theory.