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Generalized Solutions to Monge–Ampère Equations

  • Cristian E. Gutiérrez
Chapter
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Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 89)

Abstract

Let \(\Omega \) be an open subset of \(\mathbb{R}^{n}\) and \(u: \Omega \rightarrow \mathbb{R}\). Given \(x_{0} \in \Omega \), a supporting hyperplane to the function u at the point (x0,u(x0)) is an affine function (x) = u(x0) + p ⋅ (xx0) such that u(x) ≥ (x) for all \(x \in \Omega.\)

Keywords

Nonhomogeneous Dirichlet Problem Det Du Strict Convexity Assumption Det Dv Symmetric Nonnegative Definite Matrices 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Cristian E. Gutiérrez
    • 1
  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA

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