Probabilistic Characterization of Weakly Harmonic Maps with Respect to Non-Local Dirichlet Forms

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-09 DOI:10.1007/s11118-024-10129-5

Fumiya Okazaki

引用次数: 0

Abstract

We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain discontinuous martingales on Riemannian manifolds from the image of symmetric stable processes under fractional harmonic maps in a weak sense. Based on this characterization, we also consider the continuity of weakly harmonic maps along the paths of Markov processes and describe the condition for the continuity of harmonic maps by quadratic variations of martingales in some situations containing cases of energy minimizing maps.

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相对于非局部迪里希勒形式的弱谐波映射的概率特征

我们通过马尔可夫过程和马氏过程来描述关于非局部 Dirichlet 形式的弱调和映射。特别是，我们可以从弱意义上的分数调和映射下的对称稳定过程的图像中，得到黎曼流形上的非连续马廷式。基于这一表征，我们还考虑了弱调和映射沿马尔可夫过程路径的连续性，并描述了在某些包含能量最小映射的情况下，调和映射的二次变分马汀格的连续性条件。

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.