Some conditions quasi-correctness mixed boundary conditions

In the theory of infinitesimal bendings of surfaces the most common external communications are communications defining an infinitesimal bending of the relationship between the shift points of the edge and turning the tangent planes of the surface along the edge - mixed external relations. Such links are a generalization of the boundary conditions of generalized sliding and generalized rotation. In this paper we study infinitesimal deformation of surfaces of the second order of positive curvature with boundary subordinates on the edge of the external communication of the mixed type. At the same time, the case where a given vector field does not belong to the surface.