Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4 (2509.03217v1)

Published 3 Sep 2025 in math.AP

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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Authors (1)

Zhenyu Fan

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