Hessian estimates for the sigma-2 equation in dimension four (2305.12587v2)

Published 21 May 2023 in math.AP

Abstract: We derive a priori interior Hessian estimates and interior regularity for the $\sigma_2$ equation in dimension four. Our method provides respectively a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher $n\ge 5$ dimensions.

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