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Mean value theorems for solutions of linear partial differential equations

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Abstract

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 vectorM 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 vectorM is independent of the derivative. The main results of this paper generalize the well-known Zalcman theorem. Some corollaries are given.

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Authors and Affiliations

  1. Ukrainian State Academy of Light Industry, Kiev

    A. V. Pokrovskii

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  1. A. V. Pokrovskii
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Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 260–272, August, 1998.

This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01366.

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Pokrovskii, A.V. Mean value theorems for solutions of linear partial differential equations. Math Notes 64, 220–229 (1998). https://doi.org/10.1007/BF02310309

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