Boundary value problems for holomorphic functions on Lipschitz planar domains
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909101689143296 |
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| author | Gryc, William Lanzani, Loredana Xiong, Jue Zhang, Yuan |
| author_facet | Gryc, William Lanzani, Loredana Xiong, Jue Zhang, Yuan |
| contents | We study the $\bar\partial$ equation subject to various boundary value conditions on bounded simply connected Lipschitz domains $D\subset\mathbb C$: for the Dirichlet problem with datum in $L^p(bD, σ)$, this is simply a restatement of the fact that members of the holomorphic Hardy spaces are uniquely and completely determined by their boundary values. Here we identify the maximal data spaces and obtain estimates in the maximal $p$-range for the Dirichlet, Regularity-for-Dirichlet, Neumann, and Robin boundary conditions for $\bar\partial$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary value problems for holomorphic functions on Lipschitz planar domains Gryc, William Lanzani, Loredana Xiong, Jue Zhang, Yuan Complex Variables 30H10, 30E20, 30E25, 31A25 We study the $\bar\partial$ equation subject to various boundary value conditions on bounded simply connected Lipschitz domains $D\subset\mathbb C$: for the Dirichlet problem with datum in $L^p(bD, σ)$, this is simply a restatement of the fact that members of the holomorphic Hardy spaces are uniquely and completely determined by their boundary values. Here we identify the maximal data spaces and obtain estimates in the maximal $p$-range for the Dirichlet, Regularity-for-Dirichlet, Neumann, and Robin boundary conditions for $\bar\partial$. |
| title | Boundary value problems for holomorphic functions on Lipschitz planar domains |
| topic | Complex Variables 30H10, 30E20, 30E25, 31A25 |
| url | https://arxiv.org/abs/2402.06747 |