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arxiv: 2311.05835 · v1 · pith:IEQGODVRnew · submitted 2023-11-10 · 🧮 math.AP

Interior C² estimate for Hessian quotient equation in dimension three

Siyuan Lu This is my paper
classification 🧮 math.AP
keywords dimensionequationestimatehessianinteriorquotientsigmathree
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In this paper, we establish an interior $C^2$ estimate for the Hessian quotient equation $\left(\frac{\sigma_3}{\sigma_1}\right)(D^2u)=f$ in dimension three. A crucial ingredient in our proof is a Jacobi inequality.

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  1. Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions

    math.AP 2026-04 unverdicted novelty 5.0

    Interior C^{2} estimates hold for semi-convex solutions of σ_{3}(D^{2}u)/σₗ(D^{2}u)=1 (l=1,2) and related sum equations in arbitrary dimensions, together with rigidity results.