Boundary Regularity for Fully Nonlinear Parabolic equations on $C^{1,\mathrm{Dini}}$ Domains
We establish the boundary pointwise Lipschitz regularity on exterior $C^{1,\mathrm{Dini}}$ domains and the Hopf lemma on interior $C^{1,\mathrm{Dini}}$ domains for fully nonlinear parabolic equations by a unified perturbation method. In fact, above two regularity hold for more general solution sets, i.e., the Pucci's class $S^*(λ, Λ, f)$. Furthermore, based on the boundary pointwise Lipschitz regularity, we obtain the global ${W}^{2,δ}$ regularity on exterior $C^{1,\mathrm{Dini}}$ domains for any $0<δ<1$, which is new even for the harmonic functions.
math.AP↗