Regularity theory for a class of degenerate or singular fully nonlinear elliptic equations with Hamiltonian terms and applications

In this paper, we investigate regularity properties for viscosity solutions to a general class of degenerate or singular fully nonlinear elliptic equations with Hamiltonian terms, \[ \left\{ \begin{alignedat}{2} Φ(|Du|,x)F(D^{2}u,x)+H(|Du|,x) &=f(x) \quad && \text{in } Ω,\\ u&=g \quad && \text{on }