Regularity of elastic waves in the glancing region of \(P\) waves
The author studies the isotropic elastic equation with Dirichlet condition at the boundary. The domain \(\Omega\subset\mathbb R^3\) is exterior, \(\partial\Omega\) is analytic and \(\mathbb R^3\subset\Omega\) is strictly convex, i.e. the Gaussian curvature of \(\partial\Omega\) is positive everywhere. Then it is proved that the outgoing solutions of the problem under consideration have the Gevrey \(G_3\) regularity in the glancing region of the longitudinal waves. The proof of the main theorem of this paper relies on some investigations of Lebeau for the wave equation and on the investigation of P. D. Stefanov and G. Vodev [Duke Math. J. 78, No. 3, 677--714 (1995; Zbl 0846.35139)] for the Neumann problem in linear elasticity outside a strictly convex body.
scientific article; zbMATH DE number 1437023