The elastic wave equation of limited smoothness

Abstract

We establish a decoupling result for the $P$ and $S$ waves of linear, isotropic elasticity, in the setting of twice-differentiable Lamé parameters. Precisely, we show that the $P\leftrightarrow S$ 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.

References in corpus (1)

• Quantitative strong unique continuation for the Lamé system with less regular coefficients