Volume 15, Issue 4
The W1,0 Estimate for Strong Solutions of Fully Nonlinear Parabolic PDE's

Ning Zhu

J. Part. Diff. Eq., 15 (2002), pp. 1-12.

Published online: 2002-11

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  • Abstract
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.
  • Keywords

Fully nonlinear parabolic equations third boundary value conditions strong solutions W^{1 0}_∞ estimates

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@Article{JPDE-15-1, author = {}, title = {The W1,0 Estimate for Strong Solutions of Fully Nonlinear Parabolic PDE's}, journal = {Journal of Partial Differential Equations}, year = {2002}, volume = {15}, number = {4}, pages = {1--12}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5457.html} }
TY - JOUR T1 - The W1,0 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 > 3N + 1) strong solutions for the problem have the ^{1,0}_∞ a priori estimates.
Ning Zhu . (2019). The W1,0 Estimate for Strong Solutions of Fully Nonlinear Parabolic PDE's. Journal of Partial Differential Equations. 15 (4). 1-12. doi:
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