%0 Journal Article %T 非局部随机扩散方程解的H?lder连续性
H?lder Continuous of the Solutions to Nonlocal Stochastic Diffusion Equations %A 贾倩 %A 王伟 %J Pure Mathematics %P 3380-3394 %@ 2160-7605 %D 2023 %I Hans Publishing %R 10.12677/PM.2023.1312351 %X 本文的目标是获得非局部随机扩散方程解的H？lder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H？lder连续性，即解u属于空间C^β(D_T;L^p(Ω))。其次，通过使用尾估计，得到了L^p(Ω;C^{β^*}(D_T)中的温和解的估计。
In this paper, we aim to obtain the H？lder continuous of solutions to nonlocal stochastic equations. By using Campanato estimates and Sobolev embedding theorem, we first prove the H？lder con-tinuous of the mild solution of nonlocalstochastic diffusion equations in the sense that the solution u belongs to the space C^β(D_T;L^p(Ω)). Then by using tail estimates, we obtain the estimates of the mild solution in L^p(Ω;C^{β^*}(D_T). %K 分数布朗运动，H?lder连续性，L^∞估计，尾估计
Fractional Brownian Motion %K H?lder Continuity %K L^∞ Estimates %K Tail Estimates %U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=77505