We consider a problem occurring in a magnetostatic levitation. The problem leads to a linear PDE in a strip. In engineering literature a particular solution is obtained. Such a solution enables one to compute lift and drag forces of the levitating object. It is in agreement with the experiment. We show that such a solution is unique in a class of bounded regular functions. Moreover, as a byproduct, we obtain nonstandard uniqueness results in two linear PDEs in unbounded domains. One of them is an eigenvalue problem for the Laplacian in the strip in the nonstandard class of functions.

中文翻译：

---

无界域中的静磁悬浮和两个相关的线性偏微分方程

我们考虑静磁悬浮中出现的问题。该问题导致条带中出现线性偏微分方程。在工程文献中获得了特定的解决方案。这种解决方案使人们能够计算悬浮物体的升力和阻力。与实验相符。我们证明这样的解在一类有界正则函数中是唯一的。此外，作为副产品，我们在无界域中的两个线性偏微分方程中获得了非标准唯一性结果。其中之一是非标准类函数中带状拉普拉斯算子的特征值问题。