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Generalized Holmgren Problem for an Elliptic Equation with Several Singular Coefficients

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Abstract

It has recently been established that all fundamental solutions of a multidimensional singular elliptic equation can be expressed via the well-known multivariate Lauricella hypergeometric function. In the present paper, we prove that the generalized Holmgren problem for an elliptic equation with several singular coefficients has a unique solution and find this solution in closed form. When finding the solution, we use decomposition formulas and some contiguous relationships for the multivariate Lauricella hypergeometric function.

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  1. Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, 100170, Uzbekistan

    T. G. Ergashev

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  1. T. G. Ergashev
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Correspondence to T. G. Ergashev.

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Translated by V. Potapchouck

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Ergashev, T.G. Generalized Holmgren Problem for an Elliptic Equation with Several Singular Coefficients. Diff Equat 56, 842–856 (2020). https://doi.org/10.1134/S0012266120070046

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