Boundary Regularity for Fully Nonlinear Degenerate Elliptic Equations

This paper investigates fully nonlinear degenerate elliptic equations of the form $|Du|^γF(D^2u) = f$ with $γ>0$ {and $F(0)=0$}. Using a unified compactness and perturbation framework, we {establish} $C^1$ regularity on $C^{1,\mathrm{Dini}}$ domains and {$C^{1,α_0}$ regularity on $C^{1,α}$ domains