An Alexsandrov type theorem fork-convex functions
Copyright policy )An Alexsandrov type theorem fork-convex functions
In this note we show thatk-convex functions on ℝnare twice differentiable almost everywhere for every positive integerk>n/2. This generalises Alexsandrov's classical theorem for convex functions.
- Australian National University Australia
- University of Wollongong Australia
functions, generalized convexity, convex, Nonsmooth analysis, Continuity and differentiation questions, type, k, Science and Technology Studies, Operations with distributions and generalized functions, Abstract differentiation theory, differentiation of set functions, Engineering, theorem, twice differentiability, alexsandrov, Alexandrov theorem, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Convexity of real functions of several variables, generalizations
functions, generalized convexity, convex, Nonsmooth analysis, Continuity and differentiation questions, type, k, Science and Technology Studies, Operations with distributions and generalized functions, Abstract differentiation theory, differentiation of set functions, Engineering, theorem, twice differentiability, alexsandrov, Alexandrov theorem, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Convexity of real functions of several variables, generalizations
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