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Generalization of the Kelvin Theorem for Solutions of Elliptic Equations with Singular Coefficients and Applications

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Abstract

We prove the generalized Kelvin theorem and, based on the fundamental solutions of elliptic equations with singular coefficients, construct the Green’s functions of the first boundary value problem for such equations.

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ACKNOWLEDGMENTS

The author is grateful to the participants of the seminar headed by Acad. E.I. Moiseev at Lomonosov Moscow State University, where the results of this work were presented, for constructive, useful, and friendly discussion, and also expresses gratitude to Prof. S.M. Sitnik for indicating the paper [21] and sending its reprint.

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Authors and Affiliations

  1. Sterlitamak Branch, Institute for Strategic Studies, Sterlitamak, Bashkortostan, 453103, Russia

    K. B. Sabitov

  2. Sterlitamak Branch of Bashkir State University, Sterlitamak, Bashkortostan, 453103, Russia

    K. B. Sabitov

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  1. K. B. Sabitov
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Correspondence to K. B. Sabitov.

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Translated by V. Potapchouck

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Sabitov, K.B. Generalization of the Kelvin Theorem for Solutions of Elliptic Equations with Singular Coefficients and Applications. Diff Equat 58, 53–64 (2022). https://doi.org/10.1134/S0012266122010074

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  • DOI: https://doi.org/10.1134/S0012266122010074

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