Fundamental solution of displacement equations for a transversely isotropic elastic medium (Q512525)

In this article the author considers a fourth-order linear elliptic partial differential equation that is a generalization of the biharmonic equation. This describes the displacements of a transversely isotropic linear elastic medium. Furthermore, this equation and the corresponding inhomogeneous equation with a delta function on the right-hand side admit a basis of the Lie algebra of symmetry operators. The author finds a fundamental solution of the former equation that is invariant under the latter symmetry operators. This solution is constructed in terms of elementary functions.