Abstract
This paper obtains Hölder continuity of the mild solution to a stochastic parabolic equation defined on a bounded domain with homogeneous Dirichlet boundary condition. The Gaussian noise involved in the equation is white in time and correlated in space. The approach is based on a new Hölder-type estimate for the Green function in the domain.
Funding Statement
The research of Kai Du was partially supported by National Key R&D Program of China (No. 2018YFA0703900), by National Natural Science Foundation of China (No. 11801084), and by Natural Science Foundation of Shanghai (No. 20ZR1403600).
Citation
Ruoyang Liu. Kai Du. "Hölder continuity of solutions to the Dirichlet problem for SPDEs with spatially correlated noise." Electron. Commun. Probab. 26 1 - 13, 2021. https://doi.org/10.1214/21-ECP433
Information