The influence of lower derivatives on the solvability of the Dirichlet problem for multidimensional elliptic systems

By means of the Fourier transform, we examine the Dirichlet problem for a multidimensional elliptic system containing lower derivatives. We prove that the lower terms significantly influence the solvability of the first boundary value problem for elliptic systems of equations in contrast to the case of a single elliptic equation. The problem is reduced to a single second-order equation; the nature of the solvability of the original problem depends on the type of this equation.