Certain results on a parabolic type Monge-Ampere equation
نویسندگان
چکیده
منابع مشابه
A non local Monge-Ampere equation
We introduce a non local analog to the Monge-Ampere operator and show some of its properties. We prove that a global problem involving this operator has C solutions in the full space.
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0 < λ ≤ f ≤ Λ in Ω, and for some x ∈ Ω, Sh(x) ⊂⊂ Ω, then Sh(x) is equivalent to an ellipsoid centered at x i.e. kE ⊂ Sh(x)− x ⊂ k−1E for some ellipsoid E of volume h and for a constant k > 0 which depends only on λ,Λ, n. This property provides compactness of sections modulo affine transformations. This is particularly useful when dealing with interior C and W 2,p estimates of strictly convex so...
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A classical result of Aleksandrov allows one to estimate the size of a convex function u at a point x in a bounded domain Ω in terms of the distance from x to the boundary of Ω if R Ω det Du dx < ∞. This estimate plays a prominent role in the existence and regularity theory of the Monge-Ampère equation. Jerison proved an extension of Aleksandrov’s result that provides a similar estimate, in som...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1992
ISSN: 0022-247X
DOI: 10.1016/0022-247x(92)90262-c