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Volume 3, Issue 2
The First Boundary Value Problem for General Parabolic Monge-Ampere Equation

Wang Guanglie, Wang Wei

J. Part. Diff. Eq.,3(1990),pp.1-15

Published online: 1990-03

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  • Abstract
In this note we consider the first boundary value problem for a general parabolic Monge-Ampere equation u_t - log det(D_{ij}u) = f(x, t, u,D_2u) in Q, \quad u = φ(x, t) on ∂, Q It is proved that there exists a unique convex in x solution to the problem from C^{1+β,2+β/2}(\overline{Q}) under certain structure aod smoothness conditions (H3) - (H7).
  • Keywords

General parabolic Mange-Ampere equation first boundary value problem classical solution

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COPYRIGHT: © Global Science Press

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@Article{JPDE-3-1, author = {Wang Guanglie, Wang Wei}, title = {The First Boundary Value Problem for General Parabolic Monge-Ampere Equation}, journal = {Journal of Partial Differential Equations}, year = {1990}, volume = {3}, number = {2}, pages = {1--15}, abstract = { In this note we consider the first boundary value problem for a general parabolic Monge-Ampere equation u_t - log det(D_{ij}u) = f(x, t, u,D_2u) in Q, \quad u = φ(x, t) on ∂, Q It is proved that there exists a unique convex in x solution to the problem from C^{1+β,2+β/2}(\overline{Q}) under certain structure aod smoothness conditions (H3) - (H7).}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5794.html} }
TY - JOUR T1 - The First Boundary Value Problem for General Parabolic Monge-Ampere Equation AU - Wang Guanglie, Wang Wei JO - Journal of Partial Differential Equations VL - 2 SP - 1 EP - 15 PY - 1990 DA - 1990/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5794.html KW - General parabolic Mange-Ampere equation KW - first boundary value problem KW - classical solution AB - In this note we consider the first boundary value problem for a general parabolic Monge-Ampere equation u_t - log det(D_{ij}u) = f(x, t, u,D_2u) in Q, \quad u = φ(x, t) on ∂, Q It is proved that there exists a unique convex in x solution to the problem from C^{1+β,2+β/2}(\overline{Q}) under certain structure aod smoothness conditions (H3) - (H7).
Wang Guanglie, Wang Wei. (1990). The First Boundary Value Problem for General Parabolic Monge-Ampere Equation. Journal of Partial Differential Equations. 3 (2). 1-15. doi:
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