非局部随机扩散方程解的HO¨lder连续性  

HO¨lder Continuous of the Solutions to Nonlocal Stochastic Diffusion Equations

作　　者：贾倩 王伟 

机构地区：[1]天津师范大学数学科学学院,天津

出　　处：《理论数学》2023年第12期3380-3394,共15页Pure Mathematics

摘　　要：本文的目标是获得非局部随机扩散方程解的Hölder连续性。利用Campanato估计和Sobolev嵌入定理,首先证明了非局部随机扩散方程的温和解的Hölder连续性,即解u属于空间Cβ(DT;Lp(Ω))。其次,通过使用尾估计,得到了Lp(Ω;Cβ*(DT)中的温和解的估计。In this paper, we aim to obtain the Hölder continuous of solutions to nonlocal stochastic equations. By using Campanato estimates and Sobolev embedding theorem, we first prove the Hölder con-tinuous of the mild solution of nonlocalstochastic diffusion equations in the sense that the solution u belongs to the space Cβ(DT;Lp(Ω)). Then by using tail estimates, we obtain the estimates of the mild solution in Lp(Ω;Cβ*(DT).

关 键 词：分数布朗运动 HO¨lder连续性 L^∞估计 尾估计 

分 类 号：O17[理学—数学]