On the Fundamental Solution Matrix of the Plane Anisotropic Elasticity Theory

Abstract

An explicit expression (in polar coordinates) for the fundamental solution matrix of the Lam ́e system of the plane anisotropic theory of elasticity is given. It is shown that the operator of convolution with this matrix in a finite domain with Lyapunov boundary is bounded in the H ̈older spaces C^μ → C^(2,μ). A similar result is also established for an infinite domain in the corresponding weighted H ̈older spaces (with a power-law behavior at infinity).