Geodesic
The Mean-Value Theorem for Elliptic Operators on Stratified Sets
Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 417-426

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In this paper, an analog of the mean-value theorem for harmonic functions is proved for an elliptic operator on the stratified set of “stratified” spheres whose radius is sufficiently small. In contrast to the classical case, the statement of the theorem has the form of a special differential relationship between the mean values over different parts of the sphere. The result is used to prove the strong maximum principle.
Keywords: Green's formula, mean-value theorem, stratified sets, harmonic and subharmonic functions, strong maximum principle. 
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     author = {S. N. Oshchepkova and O. M. Penkin},
     title = {The {Mean-Value} {Theorem} for {Elliptic} {Operators} on {Stratified} {Sets}},
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S. N. Oshchepkova; O. M. Penkin. The Mean-Value Theorem for Elliptic Operators on Stratified Sets. Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 417-426. http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a9/