Some boundary value problems for elliptic equations, and the Lie algebras associated with them

The results presented in this paper are connected with the solvability of boundary value problems for second-order elliptic differential equations in a bounded region with smooth boundary. A typical feature of these problems is that the Lopatinskii conditions for them can fail to hold on very massive subsets of the boundary. The solvability properties of the problems under study turn out to be closely connected with the behavior of certain vector fields on the boundary of the region, with not only the leading homogeneous part of the boundary operator but also its first-order terms involved in the formation of the fields.
Bibliography: 18 titles.