A cauchy-type integral equation arising in potential theory^†

^†Dedicated to Professor Eberhard Hopf on the Occasion of his seventieth birthday

Abstract

This note is concerned with the integral equation

where 0<c≤1, the integral is the Cauchy principal value and φ₀(y) is a prescribed continuous function, By changing the variables, the integral equation can be transformed to that of Cauchy type, whose solution is well-known. Reverting to the original variables, an elegant closed form solution for (*) is obtained

^†Dedicated to Professor Eberhard Hopf on the Occasion of his seventieth birthday

^‡Research of this author has been supported by NSF Grant No. GP20149

^§Research of this author has been supported by Atomic Energy Commission Contract No.(30-1)3869

^†Dedicated to Professor Eberhard Hopf on the Occasion of his seventieth birthday

^‡Research of this author has been supported by NSF Grant No. GP20149

^§Research of this author has been supported by Atomic Energy Commission Contract No.(30-1)3869

Notes

^†Dedicated to Professor Eberhard Hopf on the Occasion of his seventieth birthday

^‡Research of this author has been supported by NSF Grant No. GP20149

^§Research of this author has been supported by Atomic Energy Commission Contract No.(30-1)3869