Consider a 2-d laplace equation $\Delta\Theta(x,z)=0$ with a corrugated boundary $ \Theta(x,f(x))=\Theta_0$. You can assume $f(x)$ to be a sinusoidal function.
1.My idea is to set $p=z-f(x)$. But then how to transform my laplace equation into the new coordinate $(x,p)$? Kind of get lost in applying the chain rules.
2.If there is a better way to solve this problem please do let me know.
Thanks a lot.