Uniform estimates for the canonical solution to the $\bar\partial$-equation on product domains
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866910970826194944 |
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| author | Dong, Robert Xin Pan, Yifei Zhang, Yuan |
| author_facet | Dong, Robert Xin Pan, Yifei Zhang, Yuan |
| contents | We obtain uniform estimates for the canonical solution to $\bar\partial u=f$ on the Cartesian product of bounded planar domains with $C^2$ boundaries, when $f$ is continuous up to the boundary. This generalizes Landucci's result for the bidisc toward higher dimensional product domains. In particular, it answers an open question of Kerzman for continuous datum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_14484 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Uniform estimates for the canonical solution to the $\bar\partial$-equation on product domains Dong, Robert Xin Pan, Yifei Zhang, Yuan Complex Variables Analysis of PDEs Primary 32A25, Secondary 32A26, 32W05 We obtain uniform estimates for the canonical solution to $\bar\partial u=f$ on the Cartesian product of bounded planar domains with $C^2$ boundaries, when $f$ is continuous up to the boundary. This generalizes Landucci's result for the bidisc toward higher dimensional product domains. In particular, it answers an open question of Kerzman for continuous datum. |
| title | Uniform estimates for the canonical solution to the $\bar\partial$-equation on product domains |
| topic | Complex Variables Analysis of PDEs Primary 32A25, Secondary 32A26, 32W05 |
| url | https://arxiv.org/abs/2006.14484 |