The Neumann boundary value problem for the Poisson equation is explicitly solved under a natural compatibility condition for the data in a particular planar circular rectangle. The case studied here is different from regular cases as the normalization condition for the Neumann function given as an integral is divergent. Hence, no normalization condition for the Neumann problem is available and the solution, if it exists, is only given up to an additive constant.

中文翻译：

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平面圆形矩形中泊松方程的诺依曼问题

Poisson 方程的 Neumann 边值问题在特定平面圆形矩形中的数据的自然兼容性条件下明确求解。这里研究的案例不同于常规案例，因为作为积分给出的诺依曼函数的归一化条件是发散的。因此，没有适用于 Neumann 问题的归一化条件，如果存在，则仅将解提供给一个加性常数。