The Fractional Laplacian with Reflections

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.