The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,σ}$ open sets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912497994301440 |
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| author | Kim, Kyeong-Hun Ryu, Junhee |
| author_facet | Kim, Kyeong-Hun Ryu, Junhee |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,σ}$ open sets Kim, Kyeong-Hun Ryu, Junhee Probability Analysis of PDEs 60H15, 35R60, 35B65, 45K05 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. |
| title | The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,σ}$ open sets |
| topic | Probability Analysis of PDEs 60H15, 35R60, 35B65, 45K05 |
| url | https://arxiv.org/abs/2507.17166 |