The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,σ}$ open sets
Year: 2025
Type: preprint
Abstract: This paper provides a comprehensive Sobolev regularity theory for the Dirichlet problem of stochastic partial differential equations in $C^{1,σ}$ open sets. We consider substantially large classes of nonlocal operators and generalized Gaussian noise. Our main results include the existence and uniqueness of strong solutions in weighted Sobolev spaces, along with maximal $L_p$-regularity estimates for the solutions.
Source: arXiv (Cornell University)
Authors: Kim, Kyeong-Hun, Ryu, Junhee
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414878465
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