Preprint

Generalized Holmgren Problem for an Elliptic Equation withSeveral Singular Coefficients

Tuhtasin ErgashevRomanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, 100170, Uzbekistan

Differential Equationsjournal2020en

ABI

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.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Iterative Methods for Nonlinear Equations

Identifiers

DOI: 10.1134/s0012266120070046

Citations and references

Cited by 017 references

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