Boundary regularity of stochastic PDEs

M. Gerencser, Annals of Probability 47 (2019) 804–834.

Journal Article | Published | English
Department
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.
Publishing Year
Date Published
2019-03-01
Journal Title
Annals of Probability
Volume
47
Issue
2
Page
804-834
ISSN
IST-REx-ID

Cite this

Gerencser M. Boundary regularity of stochastic PDEs. Annals of Probability. 2019;47(2):804-834. doi:10.1214/18-AOP1272
Gerencser, M. (2019). Boundary regularity of stochastic PDEs. Annals of Probability, 47(2), 804–834. https://doi.org/10.1214/18-AOP1272
Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” Annals of Probability 47, no. 2 (2019): 804–34. https://doi.org/10.1214/18-AOP1272.
M. Gerencser, “Boundary regularity of stochastic PDEs,” Annals of Probability, vol. 47, no. 2, pp. 804–834, 2019.
Gerencser M. 2019. Boundary regularity of stochastic PDEs. Annals of Probability. 47(2), 804–834.
Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” Annals of Probability, vol. 47, no. 2, Institute of Mathematical Statistics, 2019, pp. 804–34, doi:10.1214/18-AOP1272.

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