TY - JOUR
T1 - The W<sup>1,0</sup><sub>∞</sub> Estimate for Strong Solutions of Fully Nonlinear Parabolic PDE's
JO - Journal of Partial Differential Equations
VL - 4
SP - 1
EP - 12
PY - 2002
DA - 2002/11
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5457.html
KW - Fully nonlinear parabolic equations
KW - third boundary value conditions
KW - strong solutions
KW - W^{1
KW - 0}_∞ estimates
AB -  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 &gt; 3N + 1) strong solutions for the problem have the ^{1,0}_∞ a priori estimates.