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

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

2009-08-03

arxiv.org/abs/0908.0278v3

Mathematics

Functional Analysis

extensively revised and improved following the suggestions of the referee

Scientific paper

If $f$ is a function of $n$ variables that is locally $L^1$ approximable by a
sequence of smooth functions satisfying local $L^1$ bounds on the determinants
of the minors of the Hessian, then $f$ admits a second order Taylor expansion
almost everywhere. This extends a classical theorem of A.D. Alexandrov,
covering the special case in which $f$ is locally convex.

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