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1

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.

edited Nov 7 2010 at 18:46

Will Jagy
12.5k●1●26●45

asked Nov 7 2010 at 16:11

Solmaz
41●1

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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. – J.C. Ottem Nov 7 2010 at 17:35

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It can also be established by using Fourier series. – Denis Serre Nov 7 2010 at 17:38

phy.olemiss.edu/~cavaglia/courses/Phys_621/… – Will Jagy Nov 7 2010 at 19:32

Of course you can. – timur May 13 2011 at 2:57

Jeff · Answer 1 · 2011-10-11 01:19:38Z UTC

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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".

answered Oct 11 2011 at 1:19

Jeff
75●6

Laplace equation over concentric spheres

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