Asympotitcs for Some Singular Monge-Amp\`{e}re Equations
| Autor: | McCleerey, Nicholas |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given a psh function $\varphi\in\mathcal{E}(\Omega)$ and a smooth, bounded $\theta\geq 0$, it is known that one can solve the Monge-Amp\`{e}re equation $\mathrm{MA}(\varphi_\theta)=\theta^n\mathrm{MA}(\varphi)$, with some form of Dirichlet boundary values, by work of Ahag--Cegrell--Czy\.{z}--Hiep. Under some natural conditions, we show that $\varphi_\theta$ is comparable to $\theta\varphi$ on much of $\Omega$; especially, it is bounded on the interior of $\{\theta = 0\}$. Our results also apply to complex Hessian equations, and can be used to produce interesting Green's functions. Comment: 13 pages |
| Databáze: | arXiv |
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