On the Dirichlet problem for generalized Lamé–Navier systems in Clifford analysis

The Clifford algebra language allows us to consider natural generalizations of the Lamé–Navier system. The aim of this paper is to study the Dirichlet problem for these generalized elastic systems involving the so-called structural sets. In general, it is shown that the well-posedness for the problem fails, which reveals an important difference with the classical Dirichlet problem for the equilibrium equation.