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I'm in a search for information on the topic to devise a strategy of solving H. equation in N dimensions with Dirichlet - von Neumann type of boundary conditions. I'm assured that problem can be solved in closed form.

As far as I can see, boundary conditions in any number of dimensions are always given on hypersurface - that is N-1 subspace. Is this trivial generalization correct?

Furthermore, I read somewhere that H. equation is separable in 11 coordinate systems in 3D. Is this true? How does this number depends on N? I have a gut-feeling that number of separable coord. systems has to do something with number of hypersurfaces one can build by taking section of flat N dimensional space and (N+1) D cone and number of coordinate systems one can make using such surfaces - but, as always, this is probably already solved ... so I ask first =)

Any clue on the topic, paper or opinion is more than welcome ...

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# Helmholtz equation in N dimensions

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