An extension of Alexandrov's theorem on second derivatives of convex functions

DOI10.1016/j.aim.2011.07.002zbMath1230.46036arXiv0908.0278OpenAlexW2963445445MaRDI QIDQ643434

Joseph Howland Guthrie Fu

Publication date: 28 October 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.0278

zbMATH Keywords

Sobolev spacesconvex functionsweak derivativessecond derivativeAleksandrov's theorem

Mathematics Subject Classification ID

Fréchet and Gateaux differentiability in optimization (49J50) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Convexity of real functions of several variables, generalizations (26B25) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (5)

Currents carried by the subgradient graphs of semi-convex functions and applications to Hessian measures ⋮ Piecewise linear approximation of smooth functions of two variables ⋮ Normal cycles and curvature measures of sets with d.c. boundary ⋮ Piecewise linear approximation of smooth functions of two variables ⋮ Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds

Cites Work

• A geometrical approach to monotone functions in \(\mathbb{R}^n\)
• Some Rigidity Results Related to Monge–Ampèere Functions
• Shorter Notes: A Remark on the Nonuniqueness of Tangent Cones
• Applications of analysis on nilpotent groups to partial differential equations
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