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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