Boundary integral representation for Beltrami vector fields

Method of weighted residuals is used for developing of the boundary integral representation for a solenoidal vector field. It is shown that the solenoidal vector in an arbitrary point of domain can be expressed through its values and curls of the different order on the boundary domain. Boundary integral representation for the linear Beltrami vector fields are obtained. The boundary integral equations of the second kind for the solving of the boundary value problems of the second kind are received. It is marked that the given integral equations allow the effective numerical solving. Shown that in the case boundary value problem of the first kind solution can be obtained by quadratures. Showing the relationship between Beltrami vector fields and the solutions of the first boundary value problem for the Helmholtz equation.