The W1,0∞ Estimate for Strong Solutions of Fully Nonlinear Parabolic PDE's (Journal of Partial Differential Equations, 2020)
In this paper, we deal with the following fully nonlinear partial differential equation of parabolic type F(x, t, u,Du,D²u) + u_t = 0 in Q_T with the third boundary value conditions. We prove that under some structure conditions on F, the W^{2,1}_p (p > 3N + 1) strong solutions for the problem have the ^{1,0}_∞ a priori estimates.