Boundary $ C^{1}$ regularity for degenerate fully nonlinear elliptic equations on $ C^{2} $ domain

In this article, we establish global regularity results ($C^{0,\gamma}$, $C^{0,1}$ and $C^{1}$ estimates) for a class of degenerate fully nonlinear equation on $C^{2}$-domain. This corresponds to the boundary counterpart of the interior $C^{1}$ regularity results by \cite{APPT22} and \cite{AN25}. By example we show that $C^{1,\alpha}$ regularity of boundary datum is sharp within the scale of H\"{o}lder spaces. As a byproduct, we also provide global $C^{1,\beta}$ regularity for a class singular fully nonlinear equation.