Hi,

in which sobolev spaces $\displaystyle H^{1,p}(\Omega)$, $\displaystyle \ 1\leq p\leq \infty$, are the functions

a) $\displaystyle u(x)=x^\frac{3}{2}\sin\left ( \tfrac{1}{x} \right )$ with $\displaystyle \Omega=(0,1) $

b) $\displaystyle u(x)= \left |\ln x \right |^{-1} $ with $\displaystyle \Omega=\left ( 0, \frac{1}{2} \right ) $ ?

So, do I have to find out in which spaces $\displaystyle L^p(\Omega)$ the functions above has a first weak derivative?

And if yes: How can I find it out?

Thanks in advance,

Alexander