Schauder estimates for stochastic transport-diffusion equations with Levy processes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:474

Article

Wei, Jinlong¹  Duan, Jinqiao²  Lv, Guangying^3,4 

[1] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Hubei, Peoples R China

[2] IIT, Dept Appl Math, Chicago, IL 60616 USA

[3] Henan Univ Kaifeng, Inst Appl Math, Henan 475001, Peoples R China

[4] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

关键词: Heat kernel;    Non-Gaussian Levy noise;    Schauder estimate;    Stochastic partial differential equation;    Transport and diffusion;   

DOI  :  10.1016/j.jmaa.2018.12.066

来源: Elsevier

【 摘 要 】

In this study, we consider a transport-diffusion equation with Levy noise and Holder continuous coefficients. By using the heat kernel estimates, we derive the Schauder estimates for the mild solutions. Moreover, when the transport term vanishes and p = 2, we show that the Holder index in the space variable is optimal. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free