Eigenvalues for the Laplace Operator in the Interior of an Equilateral Triangle
Eigenvalues for the Laplace Operator in the Interior of an Equilateral Triangle
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DOI：
10.1007/s40315-013-0038-7
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发表时间：
2014-05-01
影响因子：
2.1
通讯作者：
Kalimeris, K.
中科院分区：
文献类型：
--
作者：
Fokas, A. S.;Kalimeris, K.
Lam首先得到了等边三角形内部Dirichlet、Neumann和Robin问题的拉普拉斯算子的特征值。在这里，我们提出了一个简单的，统一的方法来重新推导上述结果，并获得了斜罗宾和某些庞加莱问题的特征值。显式公式的庞加莱，本征值产量，通过适当的限制，有关公式的斜罗宾，罗宾，诺依曼和狄利克雷本征值。这里介绍的方法是基于所谓的整体关系，这是最近在文献中显示的分析，提供了一个有效的工具，边值问题的研究。
The eigenvalues of the Laplace operator for the Dirichlet, Neumann and Robin problems in the interior of an equilateral triangle were first obtained by Lam,. Here, we present a simple, unified approach for rederiving the above results and also obtain the eigenvalues for the oblique Robin and for certain Poincar, problems. The explicit formula for the Poincar, eigenvalues yields, via appropriate limits, the relevant formulae for the oblique Robin, Robin, Neumann and Dirichlet eigenvalues. The method introduced here is based on the analysis of the so-called global relation, which as shown recently in the literature, provides an effective tool for the study of boundary value problems.