With the help of Cauchy-type integrals, a new derivation of integral equations for solving logarithmic potential problems is given. A variant of the inverse logarithmic potential problem with two starlike solutions is analyzed; it contains fewer parameters than those considered by I.M. Rapoport. A criterion for the interior simple layer potential to be identically constant is obtained.

中文翻译：

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简单层对数势的正反问题

借助于柯西型积分，给出了求解对数势问题的积分方程的新推导。分析了具有两个星形解的对数逆势问题的变体；它所包含的参数少于IM Rapoport所考虑的参数。获得用于内部简单层电势相同地恒定的标准。