Boundary value problems of singular elliptic partial differential equations

In a recent paper [6], this author has extended the method of the kernel function [1] to the boundary value problems of the generalized axially symmetric potentials This method can also be applied to a more general class of singular differential equations, namely or, equivalently, We shall derive in the sequel explicit formulas for the Dirichlet problems of (1.1) in the first quadrant of the x-y plane in terms of sufficiently smooth boundary data, and obtain an error-bound for their approximate solutions. We shall also indicate how the Neumann problem can be solved.

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