Hölder regularity of the $\bar\partial-$equation on the polydisc
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912875620073472 |
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| author | Loo, Yu Jun Tumanov, Alexander |
| author_facet | Loo, Yu Jun Tumanov, Alexander |
| contents | In this note, we show the existence of a solution operator to the $\bar\partial-$equation in the polydisc that preserves Hölder regularity. This solution operator is constructed using Henkin's formula. It is a well-known fact that solution operators to the $\bar\partial-$equation on product domains do not improve Hölder regularity. Hence, this solution operator is optimal in that regard. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_04484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hölder regularity of the $\bar\partial-$equation on the polydisc Loo, Yu Jun Tumanov, Alexander Complex Variables Analysis of PDEs In this note, we show the existence of a solution operator to the $\bar\partial-$equation in the polydisc that preserves Hölder regularity. This solution operator is constructed using Henkin's formula. It is a well-known fact that solution operators to the $\bar\partial-$equation on product domains do not improve Hölder regularity. Hence, this solution operator is optimal in that regard. |
| title | Hölder regularity of the $\bar\partial-$equation on the polydisc |
| topic | Complex Variables Analysis of PDEs |
| url | https://arxiv.org/abs/2301.04484 |