Regular boundary points and the Dirichlet problem for elliptic equations in double divergence form
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912362027548672 |
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| author | Dong, Hongjie Kim, Dong-ha Kim, Seick |
| author_facet | Dong, Hongjie Kim, Dong-ha Kim, Seick |
| contents | We study the Dirichlet problem for a second-order elliptic operator $L^*$ in double divergence form, also known as the stationary Fokker-Planck-Kolmogorov equation. Assuming that the leading coefficients have Dini mean oscillation, we establish the equivalence between regular boundary points for the operator $L^*$ and those for the Laplace operator, as characterized by the classical Wiener criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regular boundary points and the Dirichlet problem for elliptic equations in double divergence form Dong, Hongjie Kim, Dong-ha Kim, Seick Analysis of PDEs We study the Dirichlet problem for a second-order elliptic operator $L^*$ in double divergence form, also known as the stationary Fokker-Planck-Kolmogorov equation. Assuming that the leading coefficients have Dini mean oscillation, we establish the equivalence between regular boundary points for the operator $L^*$ and those for the Laplace operator, as characterized by the classical Wiener criterion. |
| title | Regular boundary points and the Dirichlet problem for elliptic equations in double divergence form |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.03137 |