Global $C^1$ regularity for degenerate fully nonlinear elliptic equations

Abstract

In this paper, we prove global $C^1$ regularity for Dirichlet problem of a class of degenerate fully nonlinear elliptic equations on $C^2$ domain. This corresponds to the boundary counterpart of the interior $C^1$ regularity results by \cite{APPT22} and \cite{AN25}. By an example, we show that $C^{1,\alpha }$ regularity of boundary datum is sharp within the scale of Hölder spaces. Furthermore, we also provide boundary $C^{1,\beta }$ regularity for a class of singular fully nonlinear elliptic equations.

We revised some details in Section 2