\(C^{2,\alpha}\) estimates for solutions to almost linear elliptic equations (Q2032099)

This paper proposes an a priori interior \(C^{2,\alpha}\) estimate for viscosity solution of the non-linear, uniformly elliptic equation: \[F(D^2u)=f(x),\] where \(f(x)\in C^{\alpha}\) and \(F\) is almost linear with constant \(\epsilon\): \[\|DF(M)-DF(N)\|\leq \epsilon \] for all \(M,N\in S_n\), where \(S_n\) is the space of all real symmetric \(n\times n\) matrices.