Boundary regularity for double phase gradient-degenerate fully nonlinear elliptic equations

We investigate a class of equations involving fully nonlinear degenerate elliptic operators with a Hamiltonian term. A distinctive feature of this class is that the degeneracy arises both from the operator itself and from a variable-exponent double phase gradient structure. We first prove a comparison principle for viscosity subsolutions and supersolutions. Using an adapted Ishii–Lions “doubling of variables” method, we obtain interior Hölder regularity for viscosity solutions. Moreover, under suitable structural conditions, we extend these Hölder regularity estimates up to the boundary.