The hessian of max

Question

I was trying to understand the Hessian matrix. I asked this question what is the the hessian of the max and the min of two given functions. My question is the following : what is the exact expression of this $\operatorname{Hess}(\max(u,v))$?

Answer 1

$\max$ does not have partial derivatives everywhere. Where a Hessian may be defined (specifically, on the set $\{(x,y)\in\Bbb R^2\,:\, x\ne y\}$), it's $\begin{pmatrix}0&0\\ 0&0\end{pmatrix}$.