In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form Lu := −[pu∇]∆ + qu, on an arbitrary, bounded time-scale T, for suitable functions p, q, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space L(Tκ), in such a way that the resulting operator is self-adjoint,...

Degenerate scales usually refer to a size effect which causes non-unique solutions of boundary integral equations for certain type of boundary value problems with a unique solution. They are closely connected to the presence of a logarithmic function in the integral kernel of the single-layer potential operator. The equations of the elasticity theory provide one of the known application fields ...