BOUNDARY REGULARITY OF STOCHASTIC PDES

• 成果类型: Article
• 署名作者: Gerencser, Mate
• 署名单位: Institute of Science & Technology - Austria
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1272
• 发表日期: 2019
• 页码: 804-834
• 关键词: partial-differential-equations; sobolev space theory; constant-coefficients; spdes

摘要

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 alpha > 0 one can find a simple 1-dimensional constant coefficient linear equation whose solution at the boundary is not alpha-Holder continuous. We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on C-1 domains are proved to be alpha-Holder continuous up to the boundary with some alpha > 0.