The Dirichlet problem for stochastic partial differential equations with nonlocal operators in C1,σ open sets

초록

This paper provides a comprehensive Sobolev regularity theory for the Dirichlet problem of stochastic partial differential equations in C1,sigma 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. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

키워드