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.
|Original language||English (US)|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Feb 1 2020|
All Science Journal Classification (ASJC) codes
- Applied Mathematics