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-Amp&#232re operator
KW -  weak (or generalized) and viscosity solution
AB -  By an involved approach a geometric measure theory is established for parabolic Monge-Amp&#232re operator acting on convex-monotone functions, the theory bears complete analogy with Aleksandrov's classical ones for elliptic Monge-Amp&#232re operator acting on convex functions. The identity of solutions in weak and viscosity sense to parabolic Monge-Amp&#232re equation is proved. A general result on existence and uniqueness of weak solution to BVP for this equation is also obtained.