相对于非局部迪里希勒形式的弱谐波映射的概率特征

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-03-09 DOI:10.1007/s11118-024-10129-5

Fumiya Okazaki

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引用次数: 0

摘要

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。

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

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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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.