article published yes Mate Gerencser author 44ECEDF2-F248-11E8-B48F-1D18A9856A87 JaMa department 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. Institute of Mathematical Statistics2019 eng 0091-1798 1705.05364 00045968190000510.1214/18-AOP1272 472804-834 Gerencser, M. (2019). Boundary regularity of stochastic PDEs. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/18-AOP1272">https://doi.org/10.1214/18-AOP1272</a> Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” <i>Annals of Probability</i>, vol. 47, no. 2, Institute of Mathematical Statistics, 2019, pp. 804–34, doi:<a href="https://doi.org/10.1214/18-AOP1272">10.1214/18-AOP1272</a>. Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2019. <a href="https://doi.org/10.1214/18-AOP1272">https://doi.org/10.1214/18-AOP1272</a>. M. Gerencser, Annals of Probability 47 (2019) 804–834. Gerencser M. Boundary regularity of stochastic PDEs. <i>Annals of Probability</i>. 2019;47(2):804-834. doi:<a href="https://doi.org/10.1214/18-AOP1272">10.1214/18-AOP1272</a> M. Gerencser, “Boundary regularity of stochastic PDEs,” <i>Annals of Probability</i>, vol. 47, no. 2. Institute of Mathematical Statistics, pp. 804–834, 2019. Gerencser M. 2019. Boundary regularity of stochastic PDEs. Annals of Probability. 47(2), 804–834. 62322019-04-07T21:59:15Z2025-07-10T11:53:17Z