  The equations of stress equilibrium and strain compatibility/incompatibility
are discussed for fields with point singularities in a planar domain. The
sufficiency (or insufficiency) of the smooth maps, obtained by restricting the
singular fields to the domain away from the singularities, in completely
characterizing the equations of equilibrium and compatibility/incompatibility
over the entire domain, is established and illustrated with examples. The
uniqueness of the solution to the stress problem of incompatible linear
elasticity, allowing for singular fields, is proved. The uniqueness fails when
the problem is considered solely in terms of the restricted maps. As
applications of our framework, a general stress solution, in response to point
supported body force and defect fields, is derived and a generalized notion of
the force acting on a defect is developed.
