Interior a Priori Estimates for Solutions of Fully Non-Linear Equations
Luis A. Caffarelli · Annals of Mathematics · 1989
ABSTRACT. We derive an a prioriC 2,α estimate for solutions of the fully non-linear elliptic equationF(D 2 u) = 0, provided the level setΣ={M|F(M)=0} satisfies: (a)Σ∩{M|TrM= t} is strictly convex for all constants t; (b) the angle between the identity matrixI and the normalFij toΣis strictly positive on the non-convex part of Σ. Moreover, we do not need any convexity assumption onF in the course of the proof for the two dimensional case, as the classical result indicates. 1.