Geodesic
Uniqueness theorem for harmonic functions
Matematičeskie zametki, Tome 3 (1968) no. 3, pp. 247-252

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If the boundary values of a function, harmonic in a sphere, and its normal derivative decrease sufficiently fast to zero as a fixed point of the sphere is approached, then the corresponding function is identically zero. This note gives an unimprovable condition on the rate of decrease for which the stated uniqueness theorem holds. 
@article{MZM_1968_3_3_a1,
     author = {V. Rao},
     title = {Uniqueness theorem for harmonic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {247--252},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_3_a1/}
}
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V. Rao. Uniqueness theorem for harmonic functions. Matematičeskie zametki, Tome 3 (1968) no. 3, pp. 247-252. http://geodesic.mathdoc.fr/item/MZM_1968_3_3_a1/