@article{6232,
abstract = {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 α>0 one can find a simple 1-dimensional constant coefficient linear equation whose solution at the boundary is not α-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 α-Hölder continuous up to the boundary with some α>0.},
author = {Gerencser, Mate},
issn = {00911798},
journal = {Annals of Probability},
number = {2},
pages = {804--834},
publisher = {Institute of Mathematical Statistics},
title = {{Boundary regularity of stochastic PDEs}},
doi = {10.1214/18-AOP1272},
volume = {47},
year = {2019},
}