On spectral stability for the fractional Laplacian perturbed by unbounded obstacles

Michael Demuth; Marcel Hansmann

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On spectral stability for the fractional Laplacian perturbed by unbounded obstacles

机译：受无界障碍干扰的分数拉普拉斯算子的谱稳定性

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In this paper we give integral conditions for the stability of the absolutely continuous spectrum for the fractional Laplacian H_0 = (-Δ)~ (α/2), whereα ∈ (0, 2), perturbed by an unbounded obstacleΓ {is contained in} R~d. We use the stochastic representation of the associated semigroups to derive conditions in terms of the capacity of certain subsets of Γ. In particular, obstacles with infinite capacity are allowed.

机译：在本文中，我们给出了分数拉普拉斯算子H_0 =（-Δ）〜（α/ 2）的绝对连续谱的稳定性的积分条件，其中α∈（0，2）受无界障碍Γ{包含在}中R〜d我们使用关联的半群的随机表示来推导根据Γ的某些子集的容量产生的条件。特别地，允许具有无限容量的障碍物。

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《Mathematische Nachrichten》 |2009年第9期|共13页
作者
Michael Demuth; Marcel Hansmann;
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正文语种 eng
中图分类数学;
关键词
Obstacle perturbation; Fractional Laplacian; Stability of the absolutely continuous spectrum;

机译：障碍物摄动;分数阶拉普拉斯算子;绝对连续谱的稳定性;

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专利

1. On spectral stability for the fractional Laplacian perturbed by unbounded obstacles [J] . Michael Demuth, Marcel Hansmann Mathematische Nachrichten . 2009,第9期

机译：受无界障碍干扰的分数拉普拉斯算子的谱稳定性
2. On a perturbed p(x)-Laplacian problem in bounded and unbounded domains [J] . Cammaroto F., Vilasi L. Journal of Mathematical Analysis and Applications . 2013,第1期

机译：关于有界和无界域中的摄动p（x）-Laplacian问题
3. Asymptotic completeness for functions of the Laplacian perturbed by potentials and obstacles [J] . Eckhard Giere Mathematische Nachrichten . 2004,第1期

机译：拉普拉斯算子的势和障碍扰动的渐近完备性
4. Asymptotic stability of nonlinear perturbed neutral linear fractional system with distributed delay [C] . M. Konstantinov, E. Madamlieva, M. Petkova, International Conference "Applications of Mathematics in Engineering and Economics" . 2021

机译：具有分布延迟的非线性扰动中性线性分数系统的渐近稳定性
5. On the Laplacian and fractional Laplacian in exterior domains, and applications to the dissipative quasi-geostrophic equation. [D] . Kosloff, Leonardo. 2012

机译：关于外部域中的拉普拉斯算子和分数阶拉普拉斯算子，及其在耗散拟地转方程中的应用。
6. Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian [O] . Dorota Bors -1

机译：分数阶Laplacian控制的非线性Dirichlet BVP的稳定性
7. Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains [O] . Changtao Sheng, Jie Shen, Tao Tang, 2020

机译：快速的傅里叶般的映射Chebyshev Spectral-Galerkin方法，对于无限域中的积分分数Laplacian的PDE

On spectral stability for the fractional Laplacian perturbed by unbounded obstacles

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