Work

A Liouville Theorem for the Real k-Hessian Equation with a One-Sided Growth Condition

Year: 2026

Type: preprint

Abstract: We establish a scale-invariant interior $C^2$ estimate for smooth solutions of the real $k$-Hessian equation. As an application, we prove that every smooth entire solution of $σ_k(D^2u)=1$ satisfying $u(x)\ge b|x|^2-B$ for some constants $b,B$ with $b>0$ is a quadratic polynomial. For smooth solutions, admissibility is forced by the growth condition. The results also hold for viscosity solutions and for weak solutions in Trudinger's sense. Admissibility is required in the latter case.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.35565

Authors: Hu, Jingchen, Jiao, Heming

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223852732

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