Geodesic
Mean value theorems for solutions of linear partial differential equations
Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 260-272

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We consider generalized mean value theorems for solutions of linear differential equations with constant coefficients and zero right-hand side which satisfy the following homogeneity condition with respect to a given vector $\mathbf M$ with positive integer components: for each partial derivative occurring in the equation, the inner product of the vector composed of the orders of this derivative in each variable by the vector $\mathbf M$ is independent of the derivative. The main results of this paper generalize the well-known Zalcman theorem. Some corollaries are given. 
@article{MZM_1998_64_2_a12,
     author = {A. V. Pokrovskii},
     title = {Mean value theorems for solutions of linear partial differential equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {260--272},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a12/}
}
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A. V. Pokrovskii. Mean value theorems for solutions of linear partial differential equations. Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 260-272. http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a12/