论文标题
无界域中的磁静态悬浮和两个相关的线性PDE
Magnetostatic levitation and two related linear PDEs in unbounded domains
论文作者
论文摘要
我们认为在磁静脉悬浮中出现问题。该问题导致条带中线性PDE。在工程文献中，获得了特定的解决方案。这样的解决方案使人们能够计算悬浮物体的升力和拖动力。它与实验一致。我们表明，这种解决方案在一系列有限的常规功能中是唯一的。此外，作为副产品，我们获得了无限制域中两个线性PDE的非标准唯一性。其中之一是非标准函数类别中拉普拉斯的特征值问题。
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.
