诺伊曼-平卡莱算子特征值的衰减率

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2023-12-22 DOI:10.1007/s11118-023-10120-6

Shota Fukushima, Hyeonbae Kang, Yoshihisa Miyanishi

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引用次数: 0

摘要

如果三维域的边界足够光滑，那么诺伊曼-平卡莱算子特征值的衰减率就是已知的，而且是最优的。在本文中，我们处理了边界不太规则的域，并根据边界的霍尔德指数推导出了诺伊曼-平卡莱特征值衰减率的定量估计值。估计值特别表明，边界的规则性越低，特征值的衰减速度就越慢。我们还证明了类似的二维估计值。这些估计值不仅适用于衰减率未知的规则性较低的边界，也适用于规则性较高的边界，本文的结果比已知结果有显著改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Decay Rate of the Eigenvalues of the Neumann-Poincaré Operator

If the boundary of a domain in three dimensions is smooth enough, then the decay rate of the eigenvalues of the Neumann-Poincaré operator is known and it is optimal. In this paper, we deal with domains with less regular boundaries and derive quantitative estimates for the decay rates of the Neumann-Poincaré eigenvalues in terms of the Hölder exponent of the boundary. Estimates in particular show that the less the regularity of the boundary is, the slower is the decay of the eigenvalues. We also prove that the similar estimates in two dimensions. The estimates are not only for less regular boundaries for which the decay rate was unknown, but also for regular ones for which the result of this paper makes a significant improvement over known results.

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.