The first boundary value problem for $(A,\vec b)$-elliptic equations

The formulation of the first boundary-value problem is given for a large class of equations in a divergent form, admitting a “fixed” degeneration on any subset of the domain in which the argument is defined.
The conditions of existence of generalized solutions of this problem are found and some theorems concerning the uniqueness and continuous dependence of solutions on the boundary data are established.