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Interior $C^2$ estimate for Hessian quotient equation in dimension three

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arxiv 2311.05835 v1 pith:IEQGODVR submitted 2023-11-10 math.AP

Siyuan Lu This is my paper · ORCID
classification math.AP
keywords dimensionequationestimatehessianinteriorquotientsigmathree
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abstract

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. Removing singularities for fully nonlinear PDEs

    math.AP 2024-11 conditional novelty 6.0 of 10

    Half-line singularities of viscosity solutions are removable for fully nonlinear elliptic PDEs with a Jacobi inequality, proven by a doubling argument; the single-side version is new.

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