Does someone have a "nice" example for a Sobolev function? I need a function in $W^{r, p}(0,1)$, besides the obvious ones like absolute value function or the squared absolute value function, preferable $r, p \in \{1, 2\}$, which I can use for a paper I write about the approximative properties of neural networks.
Edit: I have a theorem in my paper about the error approximation of Sobolev functions with neural networks. and I look at how the numerical results hold up compared to the theory. That's why I need a Sobolev function with discontinuity points, because a continious function would be to easy.