Schauder-type estimates for higher-order parabolic SPDEs (Q2021532)

Based on some known results, the authors extend results on global Hölder estimates and solvability of the deterministic Cauchy problem for 2\(m\)-order partial differential equations of parabolic type to stochastic context, and study them in a class of stochastic Hölder spaces, that is, the Hölder estimates of solutions and their spatial derivatives up to order 2\(m\) are obtained. Using this result, the existence and uniqueness of solutions can be proved. The highlight of this paper is a \(p\)-coercivity condition for Schauder theory of stochastic partial differential equations in \(L^p\)-theory, which is the generalization of coercivity condition for \(L^2\) theory.