The Dirichlet problem for stochastic partial differential equations with nonlocal operators in C^1,σ open sets

2025/07/23 by Kyeong-Hun Kim, Kim, Kyeong-Hun, Junhee Ryu +1
Computer Science · Mathematics · #35B65 #35R60 #45K05 #60H15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2507.17166

openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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