For example, if I want to calculate the $W^{1,2}$ norm of $f=|x|$, then I calculate the weak derivative of $f$, which is $$ f'(x)= \begin{cases} 1&x>0\\ -1&x<0\\ \alpha&x=0 \end{cases} $$ I'm confused about the point $x=0$, how to deal with this point?
2026-04-07 09:43:11.1775554991
What is the $L^2$ norm of a function which is any random of a point?
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