Discontinuous solutions in the classical theory of bending of plates

We present necessary and sufficient conditions for existence of a class of analytic solutions of the equations of classical theory of bending of plates in a domain formed by removing from the infinite plane a set of points belonging to an arbitrary piecewise-smooth contour. Here we assume that all the components of a solution of a given class possess the property of continuous extendability onto almost all points of the boundary of the domain and that the boundary values are locally summable functions on the boundary.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1598–1605, December, 1990.