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This is a Quantitative Study study.

October 8, 2025Open Access

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

Key Points

Strong solutions exist for the dirichlet problem in weighted sobolev spaces, meeting the demands of advanced mathematical frameworks.
The study establishes maximal L_p-regularity estimates, crucial for analyzing the behavior of solutions under various conditions.
Nonlocal operators are extensively considered, showcasing their relevance in formulating more general stochastic models.
Regularity theory is applied in C^{1,σ} open sets, which broadens the scope of potential applications in real-world scenarios.

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 Lₚ-regularity estimates for the solutions.

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