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The electrostatic problem of a nearly circular disk charged to a unit potential is considered for its solution as it serves as the most important and symbolic mixed boundary value problem for Laplace's equation with the aid of which many complicated mixed boundary value problems arising in elasticity and fluid dynamics can be handled for solution. The method used involves the utility of Green's second identity, Abel's integral equations and their inversions, along with a suitably designed perturbation scheme involving the small parameter ϵ(>0) occurring in the geometrical representation of the boundary of the nearly circular disk

A mixed boundary value problem for Laplace's equation involving a nearly circular disk