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arXiv · 2608.29484

Interior $C^{2,\alpha}$ Regularity for the Quadratic Hessian Equation

Ruosi Chen·Xingchen Zhou·Ruixuan Zhu
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Abstract

We establish interior $C^{2,\alpha}$ regularity for admissible solutions of the quadratic Hessian equation with positive $C^\alpha$ right-hand side on the full positive branch. The main ingredients are a quantitative large-trace propagation argument and an adaptive Dirichlet comparison method.

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Ruosi Chen, Xingchen Zhou, Ruixuan Zhu. 2026-08-30. Interior $C^{2,\alpha}$ Regularity for the Quadratic Hessian Equation. https://arxiv.org/abs/2608.29484

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