---
_id: '6232'
abstract:
- lang: eng
  text: '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.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Mate
  full_name: Gerencser, Mate
  id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
  last_name: Gerencser
citation:
  ama: 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>
  apa: 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>
  chicago: 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>.
  ieee: M. Gerencser, “Boundary regularity of stochastic PDEs,” <i>Annals of Probability</i>,
    vol. 47, no. 2. Institute of Mathematical Statistics, pp. 804–834, 2019.
  ista: Gerencser M. 2019. Boundary regularity of stochastic PDEs. Annals of Probability.
    47(2), 804–834.
  mla: 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>.
  short: M. Gerencser, Annals of Probability 47 (2019) 804–834.
date_created: 2019-04-07T21:59:15Z
date_published: 2019-03-01T00:00:00Z
date_updated: 2025-07-10T11:53:17Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/18-AOP1272
external_id:
  arxiv:
  - '1705.05364'
  isi:
  - '000459681900005'
intvolume: '        47'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1705.05364
month: '03'
oa: 1
oa_version: Preprint
page: 804-834
publication: Annals of Probability
publication_identifier:
  issn:
  - 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Boundary regularity of stochastic PDEs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 47
year: '2019'
...