Work

Interior estimates for Hessian quotient equations

Year: 2026

Type: preprint

Abstract: We prove interior Hessian estimates in arbitrary dimensions for admissible solutions of Hessian quotient equations with constant right-hand side, when the numerator and denominator differ in degree by one or two. Counterexamples show that this degree range is optimal. The proof combines a new nonlinear comparison function, a doubling maximum principle, and a Pogorelov estimate.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.24549

Authors: Qiu, Guohuan, Yan, Jin

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

OpenAlex ID: W7214014641

Cites: 34

Cited by: 4

Related to: 10