I am trying to show that the function $\displaystyle u(r,\theta)=r^{2/3} sin((2\theta+\pi)/3)$ defined on the domain $\displaystyle 0 \le r \le 1$ and $\displaystyle - \pi /2 \le \theta \le \pi$ is in $\displaystyle H^1(\Omega)$ but not in $\displaystyle H^2(\Omega)$.

I do not know how to show this for a function of 2 variables like this one. any idea how this is done??