On Ellipticity of Operators with Shear Mappings

Nonlocal boundary-value problems are considered, in which the main operator and the operators in the boundary conditions include the differential operators and twisting operators. A definition of the trajectory symbols for this class of problems is given. We show that the elliptic problems define Fredholm operators in the corresponding Sobolev spaces. The ellipticity condition of such nonlocal boundary-value problem is given.