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

Abstract

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.