Reduction and Exact Solutions of the 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.
متن کاملNon Linear Elliptic Theory and the Monge-Ampere Equation
The Monge-Ampere equation, plays a central role in the theory of fully non linear equations. In fact we will like to show how the Monge-Ainpere equation, links in some way the ideas comming from the calculus of variations and those of the theory of fully non linear equations. 2000 Mathematics Subject Classification: 35J15, 35J20, 35J70. When learning complex analysis, it was a remarkable fact t...
متن کاملA Localization Property at the Boundary for Monge-ampere Equation
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...
متن کاملGLOBAL W 2,p ESTIMATES FOR THE MONGE-AMPERE EQUATION
We use a localization property of boundary sections for solutions to the Monge-Ampere equation and obtain global W 2,p estimates under natural assumptions on the domain and boundary data.
متن کاملA Liouville Theorem for Solutions to the Linearized Monge-ampere Equation
We prove that global Lipschitz solutions to the linearized MongeAmpere equation Lφu := ∑ φuij = 0 must be linear in 2D. The function φ is assumed to have the Monge-Ampere measure detD2φ bounded away from 0 and ∞.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 1997
ISSN: 1776-0852
DOI: 10.2991/jnmp.1997.4.1-2.17