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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.

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    $\begingroup$ What is the question ? $\endgroup$ May 11, 2014 at 22:02
  • $\begingroup$ solve the laplace equation with the boundary condition as much as possible. $\endgroup$ May 11, 2014 at 22:35

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