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Boundary value problems of singular elliptic partial differential equations

Published online by Cambridge University Press:  18 May 2009

Chi Yeung Lo
Chi Yeung Lo
Affiliation:
Michigan State University
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 2 , September 1972 , pp. 111 - 118
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

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