The Geometric Measure Theoretical Characterization of Viscosity Solutions to Parabolic Monge-Ampere Type Equation

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Volume 6, Issue 3

Wang Rouhuai, Wang Guanglie

J. Part. Diff. Eq.,6(1993),pp.237-254

Published online: 1993-06

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Abstract

By an involved approach a geometric measure theory is established for parabolic Monge-Ampère operator acting on convex-monotone functions, the theory bears complete analogy with Aleksandrov's classical ones for elliptic Monge-Ampère operator acting on convex functions. The identity of solutions in weak and viscosity sense to parabolic Monge-Ampère equation is proved. A general result on existence and uniqueness of weak solution to BVP for this equation is also obtained.

Keywords

geometric measure theory parabolic Monge-Amp&#232re operator weak (or generalized) and viscosity solution

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@Article{JPDE-6-237, author = {Wang Rouhuai, Wang Guanglie}, title = {The Geometric Measure Theoretical Characterization of Viscosity Solutions to Parabolic Monge-Ampere Type Equation}, journal = {Journal of Partial Differential Equations}, year = {1993}, volume = {6}, number = {3}, pages = {237--254}, abstract = { By an involved approach a geometric measure theory is established for parabolic Monge-Ampère operator acting on convex-monotone functions, the theory bears complete analogy with Aleksandrov's classical ones for elliptic Monge-Ampère operator acting on convex functions. The identity of solutions in weak and viscosity sense to parabolic Monge-Ampère equation is proved. A general result on existence and uniqueness of weak solution to BVP for this equation is also obtained.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5712.html} }

TY - JOUR T1 - The Geometric Measure Theoretical Characterization of Viscosity Solutions to Parabolic Monge-Ampere Type Equation AU - Wang Rouhuai, Wang Guanglie JO - Journal of Partial Differential Equations VL - 3 SP - 237 EP - 254 PY - 1993 DA - 1993/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5712.html KW - geometric measure theory KW - parabolic Monge-Ampère operator KW - weak (or generalized) and viscosity solution AB - By an involved approach a geometric measure theory is established for parabolic Monge-Ampère operator acting on convex-monotone functions, the theory bears complete analogy with Aleksandrov's classical ones for elliptic Monge-Ampère operator acting on convex functions. The identity of solutions in weak and viscosity sense to parabolic Monge-Ampère equation is proved. A general result on existence and uniqueness of weak solution to BVP for this equation is also obtained.

Wang Rouhuai, Wang Guanglie. (1993). The Geometric Measure Theoretical Characterization of Viscosity Solutions to Parabolic Monge-Ampere Type Equation. Journal of Partial Differential Equations. 6 (3). 237-254. doi:

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