Stochastic heat equations with values in a Riemannian manifold

Michael Röckner; Bo Wu; Rongchan Zhu; Xiangchan Zhu

doi:10.4171/RLM/801

Stochastic heat equations with values in a Riemannian manifold

Michael Röckner, Bo Wu, Rongchan Zhu, Xiangchan Zhu

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

The main result of this note is the existence of martingale solutions to the stochastic heat equation (SHE) in a Riemannian manifold by using suitable Dirichlet forms on the corresponding path/loop space. Moreover, we present some characterizations of the lower bound of the Ricci curvature by functional inequalities of various associated Dirichlet forms.

源语言	英语
页（从-至）	205-213
页数	9
期刊	Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
卷	29
期	1
DOI	https://doi.org/10.4171/RLM/801
出版状态	已出版 - 2018

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Röckner, M., Wu, B., Zhu, R., & Zhu, X. (2018). Stochastic heat equations with values in a Riemannian manifold. Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni, 29(1), 205-213. https://doi.org/10.4171/RLM/801

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AU - Wu, Bo

AU - Zhu, Rongchan

AU - Zhu, Xiangchan

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KW - Functional inequality

KW - Quasi-regular Dirichlet form

KW - Ricci curvature

KW - Stochastic heat equation

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Stochastic heat equations with values in a Riemannian manifold

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