Uniformly convergent Lagrange-type approximation (Q1904182)

Formulations and solutions of practical integral equations in the field of applied mathematics have always attracted much attention from many active workers. The authors has here considered at length two of the fundamental integral equations, which are satisfied by the surface-charge density on a conductor. These equations of electrostatics are discussed in detail with particular reference to the existence questions outside of the class of continuous functions and from a much broader class that is described essentially by a general integrability criterion. Two theorems, one for each equation, are stated and proved. The solutions of the equations are also examined, specially with a stress on their continuity or otherwise.