Higher Regularity for the Signorini Problem for the Homogeneous, Isotropic Lame System

In this note we discuss the (higher) regularity properties of the Signorini problem for the homogeneous, isotropic Lame system. Relying on an observation by Schumann cite{Schumann1}, we reduce the question of the solutions and the free boundary regularity for the homogeneous, isotropic Lame system to the corresponding regularity properties of the obstacle problem for the half-Laplacian.