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摘要翻译：
分数拉普拉斯算子$-(-\triangle)^{\frac{\alpha}{2}}$出现在许多物理系统中，包括l\'evy飞行和随机界面。本文给出了该算子的一种离散化形式，它适合于处理有限区间上的边界条件。通过引入两个物理模型，即跳跃粒子和弹性弹簧，证明了边界条件的实现是正确的。然后用数值方法得到了不同边界条件下有界域上的特征值和本征函数。文中还得到了有关特征值谱结构的一些解析结果。
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英文标题：
《Fractional Laplacian in Bounded Domains》
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作者：
A. Zoia, A. Rosso, M. Kardar
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
The fractional Laplacian operator, $-(-\triangle)^{\frac{\alpha}{2}}$, appears in a wide class of physical systems, including L\'evy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalues spectrum are also obtained.
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PDF链接：
https://arxiv.org/pdf/706.1254
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