We prove that the moduli of continuity viscosity solutions to fully nonlinear parabolic partial differential equations are subsolutions suitable one space variable. As applications, we obtain sharp Lipschitz bounds and gradient estimates for with bounded initial data. This work extends multiple results Andrews Clutterbuck quasilinear equations.

We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient multi-layer neural networks, while Hessian is approximated automatic differentiation of at previous step. This methodology extends to case approach recently proposed in Huré et al. (Math ...