A note on the failure of the Faber-Krahn inequality for the vector Laplacian

David Krejcirik, Pier Domenico Lamberti, Michele Zaccaron
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Abstract

We consider a natural eigenvalue problem for the vector Laplacian related to stationary Maxwell's equations in a cavity and we prove that an analog of the celebrated Faber-Krahn inequality doesn't hold.
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关于矢量拉普拉斯不等式法布尔-克拉恩不等式失效的说明
我们考虑了与空腔中的静态麦克斯韦方程有关的矢量拉普拉斯的自然特征值问题,并证明了著名的法布尔-克拉恩不等式的类似问题并不成立。
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