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When can I assume that the solution the laplace equation (or poisson equation) is radial? That is, when can I look only at (in polar coordinates)

[tex]\frac{\partial u^2} {\partial^2 r} + \frac{1}{r} \frac{\partial u} {\partial r} = f(r,\theta)[/tex]

instead of

[tex]\frac{\partial u^2} {\partial^2 r} + \frac{1}{r} \frac{\partial u} {\partial r} + \frac{1}{r^2}\frac{\partial u^2} {\partial^2 \theta} = f(r,\theta)[/tex]

With appropriate boundary conditions of course. My guess is any time that the boundary conditions are constant in theta and f depends only on r? But I'm not really sure.

Thanks for any help!

-wumple

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# Radial solutions to laplace equation

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