Abstract
In this article, we consider a stochastic partial differential equation (SPDE) driven by Gaussian colored noise with Dirichlet, Neumann or mixed nonhomogeneous random boundary conditions when the drift and diffusion coefficients are non-Lipschitz. We prove the existence of a unique strong solution to this SPDE and obtain a comparison theorem between such SPDEs. We also study the Hölder continuity of the solution in both time and space variables, and find the dependence of the Hölder exponent on that of the Dirichlet boundary.
Funding Statement
The first author was supported by Southern University of Science and Technology Start up fund Y01286120 and NSFC (Nos. 61873325 and 11831010). The second author was supported by NSFC (No. 12061004), NSF of Ningxia (No. 2021AAC02018) and Major research project for North Minzu University (No. ZDZX201902).
Acknowledgements
Xu Yang is the corresponding author.
Citation
Jie Xiong. Xu Yang. "SPDEs with non-Lipschitz coefficients and nonhomogeneous boundary conditions." Bernoulli 29 (4) 2987 - 3012, November 2023. https://doi.org/10.3150/22-BEJ1571
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