Traction boundary value problem for anisotropic elasticity in polyhedral domains

The traction boundary value problem for anisotropic elasticity is considered. For polyhedral domains in R-3, it is proved that the displacements are Holder continuous. In the n-dimensional case, n > 3, the Holder continuity is proved for domains with conic points on the boundary. The proof is based on the study of spectrum of operator pencils associated with singularities of the boundary, which is of independent interest.