Study of plane boundary value problems in the asymmetric elasticity theory

Abstract The main relations of the two-dimensional of asymmetric elasticity theory are considered. The matrix for the fundamental solutions of these equations is constructed. In the context of two-dimensional asymmetric elasticity, the volume potential, also called logarithmic potential, is obtained, which is the analog of the volume potential, from the abstract theory of singular integral equations. In the same context, the single-layer and double-layer surface potentials are obtained, which are also analogous to the surface potentials from the classical theory of equations of integral type. For the first and the second inside problems with values to the limit are deduced the specific system of integral equations of singular type. Similar for the two outside problems with values to the limit. It is demonstrated that the index of the equations of the integral type, previously defined, is null, for all four systems of singular integral equations.