On the existence of boundary values of solutions of an elliptic equation

A test is established for the existence of a boundary value for the solution of the elliptic second order equation
$$ -\sum_{i,j=1}^n(a_{ij}(x)u_{x_i}(x))_{x_j}=f(x)-\operatorname{div}F(x), \quad x\in Q. $$
In this connection, it is proved that the solution has a property $(u\in C_{n-1}(\overline Q))$ similar to continuity with respect to all variables in $\overline Q$, and that its boundary value $u|_{\partial Q}\in L_2(\partial Q)$ is the limit in $L_2$ of the traces of the solution on surfaces in a large class (which are not necessarily “parallel” to the boundary).