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arXiv · 2509.03217

Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4

Zhenyu Fan
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Abstract

We derive a priori interior Hessian estimates and regularity for the sigma-2 Hessian equation $\sigma_{2}(D^2u)=f(x,u,Du)$ with positive $C^{1,1}$ right hand side in dimension 4. In higher dimensions, the same result holds under an additional dynamic semi-convexity condition on solutions. This generalizes Qiu's and Shankar-Yuan's results.

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Zhenyu Fan. 2025-09-03. Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4. https://arxiv.org/abs/2509.03217

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