- #1
starzero
- 20
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Many texts in deriving the fundamental solution of the Laplace equation in three dimensions start by noting that the since the Laplacian has radial symmetry that
Δu=δ(x)δ(y)δ(z)
That all that needs to be considered is
d^2u/dr^2 + 2/r du/dr = δ(r)
For r > 0 the solution given is
u= c1/r + c2
I have no trouble accepting the fact that this is a solution.
My question is by what method is the solution obtained ?
I thought to apply a Laplace transform, however no initial values for u or the derivative of u are given.
Δu=δ(x)δ(y)δ(z)
That all that needs to be considered is
d^2u/dr^2 + 2/r du/dr = δ(r)
For r > 0 the solution given is
u= c1/r + c2
I have no trouble accepting the fact that this is a solution.
My question is by what method is the solution obtained ?
I thought to apply a Laplace transform, however no initial values for u or the derivative of u are given.
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