# Mean value theorem for harmonic functions on ellipsoid

Is there any result like the mean value theorem for harmonic functions on ellipsoids (instead of sphere)?

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Yes and No. No: There is no point equidistant to every point on an ellipsoid so there is no point whose value will be given by the mean of the boundary values. Yes: If you weight the boundary values properly you can recover any interior value you like. – Aaron Hoffman Apr 11 '13 at 14:13

EDIT: I remembered incorrectly: Jensen's measure at $x$ is a measure such that $$u(x)\geq\int ud\mu$$ for all superharmonic functions. The measures I was writing about apparently have no name.