The Fractional Laplacian with Reflections

IF 1 3区数学 Q1 MATHEMATICS Potential Analysis Pub Date : 2023-11-20 DOI:10.1007/s11118-023-10111-7

Krzysztof Bogdan, Markus Kunze

引用次数: 1

Abstract

Motivated by the notion of isotropic \(\alpha \)-stable Lévy processes confined, by reflections, to a bounded open Lipschitz set \(D\subset \mathbb {R}^d\), we study some related analytical objects. Thus, we construct the corresponding transition semigroup, identify its generator and prove exponential speed of convergence of the semigroup to a unique stationary distribution for large time.

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带反射的分数阶拉普拉斯式

受各向同性\(\alpha \) -稳定lsamvy过程的概念的启发，被反射限制在有界开放Lipschitz集\(D\subset \mathbb {R}^d\)中，我们研究了一些相关的分析对象。因此，我们构造了相应的过渡半群，确定了它的产生子，并证明了该半群在大时间内收敛到唯一平稳分布的指数速度。

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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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.