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PreprintarXiv licencearXiv

The Neumann problem for stochastic partial differential equations

  • Kyeong-Hun Kim
  • Junhee Ryu
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Abstract

In this paper, we study the Neumann problem for second-order stochastic partial differential equations in the half space. The coefficients are random and merely measurable in time. We develop a class of weighted function spaces for this problem, and establish existence, uniqueness, and regularity results. In contrast to the Dirichlet problem, the Neumann problem admits solutions with improved boundary regularity under suitable assumptions on the coefficients and data.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026neumann,
  title = {{The Neumann problem for stochastic partial differential equations}},
  author = {Kyeong-Hun Kim and Junhee Ryu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24493},
  eprint = {2610.24493},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24493},
}
RIS
TY  - UNPB
TI  - The Neumann problem for stochastic partial differential equations
AU  - Kyeong-Hun Kim
AU  - Junhee Ryu
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24493
UR  - https://arxiv.org/abs/2610.24493
AB  - In this paper, we study the Neumann problem for second-order stochastic partial differential equations in the half space. The coefficients are random and merely measurable in time. We develop a class of weighted function spaces for this problem, and establish existence, uniqueness, and regularity results. In contrast to the Dirichlet problem, the Neumann problem admits solutions with improved boundary regularity under suitable assumptions on the coefficients and data.
ER  -