Generalized Solutions to Monge–Ampère Equations

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


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 \(x \in \Omega.\)


Nonhomogeneous Dirichlet Problem Det Du Strict Convexity Assumption Det Dv Symmetric Nonnegative Definite Matrices 
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© Springer International Publishing 2016

Authors and Affiliations

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

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