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Erschienen in:
1994 | OriginalPaper | Buchkapitel
Generalized Solutions of N-Dimensional Monge-Ampere Equations
verfasst von : Ilya J. Bakelman
Erschienen in: Convex Analysis and Nonlinear Geometric Elliptic Equations
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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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.