关于凸函数二阶导数的Alexandrov定理的推广
An extension of Alexandrov's theorem on second derivatives of convex functions
摘要：
如果$f$是一个$n$变量的函数，它是局部$L^1$可由一个光滑函数序列逼近的，该光滑函数序列满足Hessian行列式的局部$L^1$界，则$f$几乎处处允许二阶泰勒展开。这扩展了A.D. Alexandrov的一个经典定理，涵盖了$f$是局部凸的特殊情况。
英文摘要：
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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