Boundary pointwise regularity for fully nonlinear parabolic equations and application to the regularity of free boundaries

In this paper, we prove boundary pointwise (, ) regularity for fully nonlinear parabolic equations. In particular, we prove that if the solution and the boundary value function vanish up to order , the regularity can be lifted by order (Theorem 1.25). As an application, we give a direct and short proof of the higher regularity of the free boundaries in obstacle‐type problems (Theorem 1.30).