I am having with understanding one notation in a paper I am reading it.
The paper is about how to approximate the initial temperature for a one-dimensional body from discrete temperatures made at later times.
I know the notation for Sobolev space, and I have some books about that, but I did not find any clarification about it.
The notation is $f \in W^r(L_2)$, so I am not sure if that means $f \in W^{r,2}((0. \pi))$ which means $f$ is differential $r-times$, or somthing else?
THANK YOU.