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Sharp conditions for fully nonlinear equations with (n−1)-Hessian matrix: Part II. k-Hessian case
Abstract
We study admissible entire subsolutions and radial boundary blow-up solutions of Sk1/k[ΔuI−D2u]=f(u)+g(u)|Du|q for 1≤ 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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BibTeX
@misc{ji2026sharp,
title = {{Sharp conditions for fully nonlinear equations with $(n-1)$-Hessian matrix: Part II. $k$-Hessian case}},
author = {Jingwen Ji and Feida Jiang and Mengni Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15697},
eprint = {2610.15697},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15697},
}
RIS
TY - UNPB
TI - Sharp conditions for fully nonlinear equations with (n−1)-Hessian matrix: Part II. k-Hessian case
AU - Jingwen Ji
AU - Feida Jiang
AU - Mengni Li
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15697
UR - https://arxiv.org/abs/2610.15697
AB - We study admissible entire subsolutions and radial boundary blow-up solutions of S_k^1/k[ΔuI−D^2u]=f(u)+g(u)|Du|^q for 1≤ 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.
ER -