Boundary blow-up solutions to real $(N-1)$-Monge-Ampère equations with singular weights
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| author | Saha, Kiran Kumar Tiwari, Sweta |
| author_facet | Saha, Kiran Kumar Tiwari, Sweta |
| contents | In this paper, we study a boundary blow-up problem for real $(N-1)$-Monge-Ampère equations of the form \begin{equation}
\nonumber \left \{
\begin{aligned}
& \operatorname{\det}^{\frac{1}{N-1}}\left(ΔzI-D^{2}z\right)=K(|x|)f(z) && \text{ in } Ω,
& z(x) \to \infty \text{ as } \dist(x,\partialΩ) \to 0,
\end{aligned}
\right. \end{equation} where $Ω$ denotes a ball in $\mathbb{R}^{N} ~ (N \geq 2)$. The weight function $K$ is allowed to be singular, and the nonlinearity $f$ is assumed to satisfy a Keller-Osserman type condition. We establish the existence of infinitely many radial $(N-1)$-convex solutions to the system by employing the method of sub- and super-solutions, in conjunction with a comparison principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary blow-up solutions to real $(N-1)$-Monge-Ampère equations with singular weights Saha, Kiran Kumar Tiwari, Sweta Analysis of PDEs In this paper, we study a boundary blow-up problem for real $(N-1)$-Monge-Ampère equations of the form \begin{equation} \nonumber \left \{ \begin{aligned} & \operatorname{\det}^{\frac{1}{N-1}}\left(ΔzI-D^{2}z\right)=K(|x|)f(z) && \text{ in } Ω, & z(x) \to \infty \text{ as } \dist(x,\partialΩ) \to 0, \end{aligned} \right. \end{equation} where $Ω$ denotes a ball in $\mathbb{R}^{N} ~ (N \geq 2)$. The weight function $K$ is allowed to be singular, and the nonlinearity $f$ is assumed to satisfy a Keller-Osserman type condition. We establish the existence of infinitely many radial $(N-1)$-convex solutions to the system by employing the method of sub- and super-solutions, in conjunction with a comparison principle. |
| title | Boundary blow-up solutions to real $(N-1)$-Monge-Ampère equations with singular weights |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.12091 |