Boundary regularity of stochastic PDEs

The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary conditions can be surprisingly.and in a sense, arbitrarily.bad: as shown by Krylov [SIAM J. Math. Anal. 34 (2003) 1167.1182], for any .>0 one can find a simple 1-dimensional constant coefficient linear equation whose solution at the boundary is not -Hölder continuous. We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on C1 domains are proved to be .-Hölder continuous up to the boundary with some .>0.