find the solution of laplaces eqtn
uxx+uyy=0
(the equation is actually the upside down triangle operator, but i believe this is the same notation)
inside a sphere of radius 1 with B.C. u=z^2 for r=1
I would be tempted to try to define the sphere in spherical polar co-ordinates, so you have the surface (ie where the radius is one) defined by two varying angles. Then rewrite Del^2 u as its equivalant for the two angles, bang in the boundary condition and see where it takes you. I will see if it works tommorow and learn latex at the same time!
Also if its applied to a sphere ie a 3d shape, i would have thought u=u(u,v,w) thus Del^2 (u) would be " uxx + uyy + uzz = 0 "