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Generalized Solutions of N-Dimensional Monge-Ampere Equations

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Abstract

First of all we introduce the concepts of the normal mapping of convex functions and the R-curvature of these functions. The R-curvature of convex functions is the extension of Monge-Ampere operators to the class of all general convex functions. We study in detail the properties of the normal mapping and R-curvature of convex functions and then investigate the solvability of the Dirichlet problem for weak and generalized elliptic solutions together with uniqueness and non-uniqueness theorems for these solutions.

Keywords

  • Weak Solution
  • Convex Function
  • Dirichlet Problem
  • Convex Cone
  • Convex Domain

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  • DOI: 10.1007/978-3-642-69881-1_3
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© 1994 Springer-Verlag Berlin Heidelberg

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Bakelman, I.J. (1994). Generalized Solutions of N-Dimensional Monge-Ampere Equations. In: Convex Analysis and Nonlinear Geometric Elliptic Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69881-1_3

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  • DOI: https://doi.org/10.1007/978-3-642-69881-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69883-5

  • Online ISBN: 978-3-642-69881-1

  • eBook Packages: Springer Book Archive