Singular Solutions to the Complex Monge-Ampère Equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911991199694848 |
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| author | Wang, Jiaxiang Wang, Wenlong |
| author_facet | Wang, Jiaxiang Wang, Wenlong |
| contents | We present an explicit pluripotential and viscosity solution to the complex Monge-Ampère equation with constant right-hand side on $\mathbb D\times\mathbb C^{n-1}\,(n\geq 2)$, which lies merely in $W^{1,2}_{loc}\cap W^{2,1}_{loc}$ and is not even Dini continuous. Additionally, we exhibit two families of explicit entire toric solutions on $\mathbb C^n$ with continuous Hölder exponent $α\in(0,1)$ and $W^{2,p}_{loc}$ exponent $p\in (1,2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular Solutions to the Complex Monge-Ampère Equation Wang, Jiaxiang Wang, Wenlong Analysis of PDEs Complex Variables Differential Geometry 32W20 (Primary) 35B65 (Secondary) We present an explicit pluripotential and viscosity solution to the complex Monge-Ampère equation with constant right-hand side on $\mathbb D\times\mathbb C^{n-1}\,(n\geq 2)$, which lies merely in $W^{1,2}_{loc}\cap W^{2,1}_{loc}$ and is not even Dini continuous. Additionally, we exhibit two families of explicit entire toric solutions on $\mathbb C^n$ with continuous Hölder exponent $α\in(0,1)$ and $W^{2,p}_{loc}$ exponent $p\in (1,2)$. |
| title | Singular Solutions to the Complex Monge-Ampère Equation |
| topic | Analysis of PDEs Complex Variables Differential Geometry 32W20 (Primary) 35B65 (Secondary) |
| url | https://arxiv.org/abs/2407.21667 |