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Pure Mathematics 2023
非局部随机扩散方程解的H?lder连续性
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Abstract:
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 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 Cβ(DT;Lp(Ω)). Then by using tail estimates, we obtain the estimates of the mild solution in Lp(Ω;Cβ*(DT).
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