I would like some help with the following problem. Thanks for any help in advance.
Use spherical coordinates to find all solutions of the Laplace equation ∆u(x)=0, u∈Ω⊂R3 that depend only on the radial variable r = |x| in the two following cases: (i)Ω is a ball|x|< a and (ii)Ω is the set defined by|x|>a
If I am only looking at solutions of the Laplace equation that depend on r alone, then my solution is u=A+B(1/r), but the I am unsure how to make use of the two cases.