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arXiv · 1911.04246

Hessian estimate for semiconvex solutions to the sigma-2 equation

Ravi Shankar·Yu Yuan
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Abstract

We derive a priori interior Hessian estimates for semiconvex solutions to the sigma-2 equation. An elusive Jacobi inequality, a transformation rule under the Legendre-Lewy transform, and a mean value inequality for the still nonuniformly elliptic equation without area structure are the key to our arguments. Previously, this result was known for almost convex solutions.

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Ravi Shankar, Yu Yuan. 2019-11-07. Hessian estimate for semiconvex solutions to the sigma-2 equation. https://arxiv.org/abs/1911.04246

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