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arXiv · 0908.0278

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

Joseph H. G. Fu
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Abstract

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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Joseph H. G. Fu. 2009-08-03. An extension of Alexandrov's theorem on second derivatives of convex functions. https://arxiv.org/abs/0908.0278

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