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arXiv · 2610.15697

Sharp conditions for fully nonlinear equations with $(n-1)$-Hessian matrix: Part II. $k$-Hessian case

Jingwen Ji·Feida Jiang·Mengni Li
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Abstract

We study admissible entire subsolutions and radial boundary blow-up solutions of $S_k^{\frac1k}[ΔuI-D^2u]=f(u)+g(u)|Du|^q$ for $1\leq k<n$, continuing our study of the determinant case $k=n$ in Part I. Under structural assumptions on the continuous, non-decreasing coefficients $f$ and $g$, we establish necessary and sufficient conditions for the existence of entire subsolutions when $q<2$. Our results cover the non-Lipschitz case $0<q<1$ with a possibly vanishing zero-order term, the gradient-singular case $q<0$, and sign-changing gradient coefficients. We also characterize finite-radius blow-up of radial solutions and derive two-sided estimates for the blow-up radius, as well as pointwise upper bounds for their profiles in terms of inverse Keller--Osserman functions.

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Jingwen Ji, Feida Jiang, Mengni Li. 2026-10-11. Sharp conditions for fully nonlinear equations with $(n-1)$-Hessian matrix: Part II. $k$-Hessian case. https://arxiv.org/abs/2610.15697

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