Boundary Hölder gradient estimates for fully nonlinear degenerate or singular parabolic equations

Abstract: We study boundary regularity of viscosity solutions to fully nonlinear degenerate or singular parabolic equations. The gradient-dependent degeneracy or singularity, along with the time derivative, introduces significant challenges beyond the elliptic case. By combining compactness methods, barrier constructions, regularization techniques, and the boundary regularity of small perturbation solutions, we establish boundary H\"older gradient estimates that unify and extend previous results.