Hölder continuous of the solutions to stochastic nonlocal heat equations

Abstract

In this paper, we aim to obtain the Hölder continuous of solutions to stochastic nonlocal heat equations. By using Campanato estimates and Sobolev embedding theorem, we first prove the Hölder continuous of the mild solution of stochastic nonlocal diffusion equations locally in Rd in the sense that the solution u belongs to the space Cγ(DT;Lp(Ω)). Then by using tail estimates, we obtain the estimates of the mild solution in Lp(Ω;Cγ(DT)). Lastly, we prove the Hölder continuous of the mild solution on bounded domain.