On a singular boundary value problem for the Poisson equation

A problem which arises from a classical problem of electrostatics of determining the potential of a field created by charged point objects which can be point charges, dipoles, or infinite combinations of multipoles of various orders is studied. There are similar problems in mechanics and other areas of physics. In a mathematical formulation it reduces to a boundary value problem for the Poisson equation in a bounded domain with excised singular points at which the solution and the right side of the equation may have singularities of arbitrary order, in particular, of the type of an essential singularity of analytic functions (with no loss of generality the case of a single singular point is considered).