ANZIAM  J.  46 (2004), 85-93
E. R. Love's integral equation for the circular plate condenser

Edgar Reich
  School of Mathematics
  University of Minnesota
  Minneapolis, Minnesota 55455

In a classical paper, E. R. Love considered a certain function defined by a singular integral which is harmonic outside a circular disk. Love's objective was to derive a simple integral equation whose solution leads to a useful formula for the capacitance of the condenser consisting of two parallel circular plates. We close a gap in Love's derivation by finding a new nonsingular representation of Love's singular integral which permits one to draw the required conclusions about its boundary values and thereby establishes the correctness of Love's expression for the capacitance.
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