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