Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere
Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere
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DOI：
10.3934/dcds.2020040
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Yoshitsugu Kabeya
中科院分区：
文献类型：
--
作者：
Yoshitsugu Kabeya
本文研究了球面区域上Laplace-Beltrami算子在齐次Neumann条件下的特征值。特别是，我们调查的情况下，当域是一个大的带状，并让该区域更大，使该区域覆盖整个领域作为一个限制。我们根据区域的膨胀率讨论了特征值的行为。
We consider the eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a spherical domain. Especially, we investigate the case when the domain is a large zonal one and letting the zone larger so that the zone covers the whole sphere as a limit. We discuss the behavior of eigenvalues according to the rate of expansion of the zone.