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arXiv · 2608.26503

Regularity for convex viscosity solutions of $\sigma_3$ equation

Ruosi Chen·Yannan Liu·Xingchen Zhou
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Abstract

We prove interior $C^2$ regularity for convex viscosity solutions of the $3$-Hessian equation $\sigma_3(D^2u)=f(x)$ with $f\in C^{0,1}, \inf f>0$, under a strict $3$-convexity condition on $u$.

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Ruosi Chen, Yannan Liu, Xingchen Zhou. 2026-08-27. Regularity for convex viscosity solutions of $\sigma_3$ equation. https://arxiv.org/abs/2608.26503

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