Fourier multipliers for nonlocal Laplace operators
Fourier multipliers for nonlocal Laplace operators
复制标题
非局部拉普拉斯算子的傅里叶乘子
DOI：
10.1080/00036811.2019.1692134
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发表时间：
2018
影响因子：
1.1
通讯作者：
Nathan Albin
中科院分区：
文献类型：
--
作者：
Bacim Alali;Nathan Albin
摘要针对标量场定义的非局部周动力型拉普拉斯算子，建立了傅里叶乘子分析方法。傅里叶乘数是通过积分表示给出的。我们证明了傅里叶乘子的积分表示是通过一个统一的通用公式在任何空间维度n的超几何函数中明确地识别出来的。利用的渐近分析来确定傅里叶乘子的渐近行为为。我们证明了当周动力拉普拉斯函数具有可积核时乘子是有界的，当核是奇异时乘子是发散的。用维数n、积分核和周动力拉普拉斯非局域性明确地给出了边界和衰减率。在周期集合中应用渐近分析证明了周期泊松方程的正则性结果，并证明了其解收敛于经典泊松方程的解。
ABSTRACT Fourier multiplier analysis is developed for nonlocal peridynamic-type Laplace operators, which are defined for scalar fields in . The Fourier multipliers are given through an integral representation. We show that the integral representation of the Fourier multipliers is recognized explicitly through a unified and general formula in terms of the hypergeometric function in any spatial dimension n. Asymptotic analysis of is utilized to identify the asymptotic behavior of the Fourier multipliers as . We show that the multipliers are bounded when the peridynamic Laplacian has an integrable kernel and diverge when the kernel is singular. The bounds and decay rates are presented explicitly in terms of the dimension n, the integral kernel and the peridynamic Laplacian nonlocality. The asymptotic analysis is applied in the periodic setting to prove a regularity result for the peridynamic Poisson equation and, moreover, show that its solution converges to the solution of the classical Poisson equation.