A necessary and sufficient condition for Hölder-class solutions to the complex Monge--Ampère equation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909920054476800 |
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| author | Banik, Annapurna |
| author_facet | Banik, Annapurna |
| contents | We provide a necessary and sufficient condition for the existence of Hölder continuous solutions to the complex Monge--Ampère equation on bounded domains in $\mathbb{C}^n$. This condition is motivated by a paper by S.-Y. Li. We also prove a result on the regularity of solutions to the complex Monge--Ampère equation on general $B$-regular domains in $\mathbb{C}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A necessary and sufficient condition for Hölder-class solutions to the complex Monge--Ampère equation Banik, Annapurna Complex Variables Analysis of PDEs 32W20, 32U05 (Primary) 32U10, 32T40 (Secondary) We provide a necessary and sufficient condition for the existence of Hölder continuous solutions to the complex Monge--Ampère equation on bounded domains in $\mathbb{C}^n$. This condition is motivated by a paper by S.-Y. Li. We also prove a result on the regularity of solutions to the complex Monge--Ampère equation on general $B$-regular domains in $\mathbb{C}^n$. |
| title | A necessary and sufficient condition for Hölder-class solutions to the complex Monge--Ampère equation |
| topic | Complex Variables Analysis of PDEs 32W20, 32U05 (Primary) 32U10, 32T40 (Secondary) |
| url | https://arxiv.org/abs/2511.18605 |