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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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