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Is there a closed formula for the solution of Dirichlet problem ($\Delta u=0$) for annulus $r <|x| < R$, $x \in R^n$ (n>2), with two given boundary value functions, $f$ over $|x|=r$ and $g$ over $|x|=R$?

If the answer is yes, please give the formula or a reference for it.

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    $\begingroup$ It seems that a formula could be derived using generalized cylindrical cordinates, seperation of variables and a lot of calculation, just like in the 2D case. $\endgroup$
    – J.C. Ottem
    Commented Nov 7, 2010 at 17:35
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    $\begingroup$ It can also be established by using Fourier series. $\endgroup$
    – Denis Serre
    Commented Nov 7, 2010 at 17:38
  • $\begingroup$ phy.olemiss.edu/~cavaglia/courses/Phys_621/… $\endgroup$
    – Will Jagy
    Commented Nov 7, 2010 at 19:32
  • $\begingroup$ Of course you can. $\endgroup$
    – timur
    Commented May 13, 2011 at 2:57

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This is exercise 2.5 on page 29 in Gilbarg and Trudinger's book "Elliptic Partial Differential Equations of Second Order".

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