On strongly coupled multidimensional elliptic systems

The article investigates the Dirichlet problem in a half-space for an elliptic system as per Petrovsky of three equations with three unknown functions depending on three independent variables. Conditions for violation of the Noetherian property of the problem in a concrete half-space are found. It is shown that the strong connectedness of the system does not imply the violation of the Noetherian property of the Dirichlet problem in any half-space.