We provide a proof of the following well known fact.

Theorem. There is no solution to

I found this proof in a paper due to Y.Y. Li published in *Commun. Math. Phys.* in 1999 [here]. Before deriving the proof, let us recall the following notation known as the sphere mean in the literature. In we denote the integral

by . We call the average of on the sphere of radius , or sphere mean of a function around the origin. In this context, we simply have

.

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