reference request about sobolev space and BV space

Question

I am studying Sobolev Space and BV space by using Leoni's and Evans & Gariepy's book. I was wondering that where can I find some explicit example and some computational question of those space. A question like compute whether $$ u(x)=x^2\sin(1/x^2)$$ is BV, Sobolev, or AC.

I know Leoni's book has some, but I am looking for more.(Especially in 1-D)

Thanks in advance!