Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Kim, Kyeong-Hun, Ryu, Junhee
Institutions: Korea University, Korea Institute for Advanced Study
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6210473723
OpenAlex ID: W7223068065