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In this paper, we deal with the following fully nonlinear partial differential equation of parabolic type F(x,t,u, Du, D2u)+ut=0 inQT with the third boundary value conditions. We prove that under some structure conditions on F, the Wp 2,1 (p ＞ 3N + 1) strong solutions for the problem have the W1,0∞ a priori estimates.