Sharp conditions for fully nonlinear equations with $(n-1)$-Hessian matrix: Part I. Monge--Ampère case
Year: 2026
Type: preprint
Abstract: We study positive $(n-1)$-convex entire subsolutions of the normalized real $(n-1)$ Monge--Ampère equation $\operatorname{det}^{\frac1n}\bigl(ΔuI-D^2u\bigr)=f(u)+g(u)|Du|^q$ in $\mathbb R^n$. Under two sets of structural assumptions on the continuous, non-decreasing coefficients $f$ and $g$, we establish necessary and sufficient conditions for the existence of entire subsolutions when $q<2-\frac1n$. Our results cover the pure-gradient degenerate case $f\equiv0$ with $0
Source: arXiv (Cornell University)
Authors: Ji, Jingwen, Jiang, Feida, Li, Mengni
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G283934269
OpenAlex ID: W7221812234