Abstract:
The main result of the present paper is the construction
of fundamental solutions for a class of multidimensional elliptic
equations with several singular coefficients. These fundamental
solutions are directly connected with multiple hypergeometric
functions and the decomposition formula is required for their
investigation which would express the multivariable hypergeometric
function in terms of products of several simpler hypergeometric
functions involving fewer variables. In this paper, such a formula
is proved instead of a previously existing recurrence formula.The
order of singularity and other properties of the fundamental
solutions that are necessary for solving boundary value problems
for degenerate second-order elliptic equations are determined.
Keywords:
multidimensional elliptic equation with several singular coefficients, fundamental solutions, decomposition formula.
Received: 13.09.2019 Received in revised form: 14.10.2019 Accepted: 04.12.2019
Bibliographic databases:
Document Type:
Article
UDC:517.956.6; 517.44
Language: English
Citation:
Tuhtasin G. Ergashev, “Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients”, J. Sib. Fed. Univ. Math. Phys., 13:1 (2020), 48–57
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\by Tuhtasin~G.~Ergashev
\paper Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 1
\pages 48--57
\mathnet{http://mi.mathnet.ru/jsfu817}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-1-48-57}
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Linking options:
https://www.mathnet.ru/eng/jsfu817
https://www.mathnet.ru/eng/jsfu/v13/i1/p48
This publication is cited in the following 10 articles:
T. G. Ergashev, A. Hasanov, T. K. Yuldashev, “Some Infinite Expansions of the Lauricella Functions and Their Application in the Study of Fundamental Solutions of a Singular Elliptic Equation”, Lobachevskii J Math, 45:3 (2024), 1072
T. G. Ergashev, Z. R. Tulakova, “A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain”, Russian Math. (Iz. VUZ), 66:7 (2022), 51–63
T. G. Ergashev, Z. R. Tulakova, “The Neumann Problem for a Multidimensional Elliptic Equation with Several Singular Coefficients in an Infinite Domain”, Lobachevskii J Math, 43:1 (2022), 199
T. G. Ergashev, “Potentsialy dlya trekhmernogo ellipticheskogo uravneniya s odnim singulyarnym koeffitsientom i ikh primenenie”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 25:2 (2021), 257–285
T. G. Ergashev, Z. R. Tulakova, “The Dirichlet problem for an elliptic equation with several singular coefficients in an infinite domain”, Russian Math. (Iz. VUZ), 65:7 (2021), 71–80
A. Hasanov, N. Djuraev, “Exact Solutions of the Thin Beam with Degrading Hysteresis Behavior”, Lobachevskii J Math, 42:15 (2021), 3637
T. G. Ergashev, N. J. Komilova, “Generalized Solution of the Cauchy Problem for Hyperbolic Equation with Two Lines of Degeneracy of the Second Kind”, Lobachevskii J Math, 42:15 (2021), 3616
T. G. Ergashev, A. Hasanov, “Holmgren problem for elliptic equation with singular coefficients”, Vestnik KRAUNTs. Fiz.-mat. nauki, 32:3 (2020), 114–126
Ergashev T.G., “Generalized Holmgren Problem For An Elliptic Equation With Several Singular Coefficients”, Differ. Equ., 56:7 (2020), 842–856
Ergashev T.G., “Potentials For Three-Dimensional Singular Elliptic Equation and Their Application to the Solving a Mixed Problem”, Lobachevskii J. Math., 41:6, SI (2020), 1067–1077
Citation in format AMSBIB
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