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

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- May 11th 2009, 08:00 PMmlemilyslaplacian
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 - May 13th 2009, 02:31 PMOnkelTom
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 "