Log-Harnack inequality for stochastic Burgers equations and applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:384

Article

Wang, Feng-Yu^2,3,4  Wu, Jiang-Lun⁴  Xu, Lihu¹ 

[1] EURANDOM, NL-5600 MB Eindhoven, Netherlands

[2] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[3] Beijing Normal Univ, Lab Math Com Sys, Beijing 100875, Peoples R China

[4] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

关键词: Stochastic Burgers equation;    Log-Harnack inequality;    Strong Feller property;    Irreducibility;    Entropy-cost inequality;   

DOI  :  10.1016/j.jmaa.2011.02.032

来源: Elsevier

【 摘 要 】

By proving an L-2-gradient estimate for the corresponding Galerkin approximations, the log-Harnack inequality is established for the semigroup associated to a class of stochastic Burgers equations. As applications, we derive the strong Feller property of the semigroup, the irreducibility of the solution, the entropy-cost inequality for the adjoint semigroup, and entropy upper bounds of the transition density. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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