On completeness of root functions of Sturm–Liouville problems with discontinuous boundary operators

We consider a Sturm–Liouville boundary value problem in a bounded domain DD of RnRn. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in DD and the boundary conditions are of Robin type on ∂D∂D. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact selfadjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types.