Interior Hessian Estimates for Semi-convex Solutions of the ${\sigma }_2/{\sigma }_1$ Equation with Lipschitz Right-Hand Sides

Ke Ji, Lichun Liang

Let $n\ge 2$ and let $u$ be a smooth 2-convex and semi-convex solution of \[ \frac{σ_2(D^2u)}{σ_1(D^2u)}=f(x). \] We prove an interior Hessian estimate depending on the Lipschitz no…