On the absence of global solutions of the Gauss equation and solutions in external areas

We consider conditions under which the Gauss equation has no solutions defined in the whole space or in areas external with respect to a ball. The absence of solutions in external areas is established in the case when the number of independent variables is more than two. In the two-dimensional case we obtain conditions ensuring the absence of global solutions of the second-order elliptic equation with variable coefficients in its linear part.