Decoupling of Modes for the Elastic Wave Equation in Media of Limited Smoothness

We establish a decoupling result for the P and S waves of linear, isotropic elasticity, in the setting of twice-differentiable Lame parameters. Precisely, we show that the P <-> S components of the wave propagation operator are regularizing of order one on L-2 data, by establishing the diagonalization of the elastic system modulo a L-2-bounded operator. Effecting the diagonalization in the setting of twice-differentiable coefficients depends upon the symbol of the conjugation operator having a particular structure.