Showing function is in sobolev space

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March 5th 2009, 06:35 AM
johnbarkwith

Showing function is in sobolev space

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??

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