10.1214/18-AOP1272
Gerencser, Mate
Mate
Gerencser
Boundary regularity of stochastic PDEs
Institute of Mathematical Statistics
2019
2019-04-07T21:59:15Z
2019-08-02T12:39:15Z
journal_article
https://research-explorer.app.ist.ac.at/record/6232
https://research-explorer.app.ist.ac.at/record/6232.json
00911798
1705.05364
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.