Asymptotics and regularity of flat solutions to fully nonlinear elliptic problems (Q2807107)

In this work the authors establish local \(C^{2,\alpha}\) regularity estimates for flat solutions to non-convex fully nonlinear elliptic equations assuming \(C^\alpha\) regularity for the coefficients and the source function. If the coefficients and the source function are only continuous, the authors prove that flat solutions are locally \(C^{1,\operatorname{Log}-\mathrm{Lip}}\). The proofs are based on a combination of geometric tangential analysis and perturbation arguments.