Hessian estimate for semiconvex solutions to the sigma-2 equation

  • Ravi Shankar
  • Yu YuanEmail author


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.

Mathematics Subject Classification

35J96 35B45 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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