International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 125-128

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

A. Chakrabarti and D. P. Manna

Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India

Received 20 February 1992; Revised 15 March 1993

Copyright © 1994 A. Chakrabarti and D. P. Manna. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.