Potentials for Three-Dimensional Singular Elliptic Equation and Their Application to the Solving a Mixed Problem

Ergashev, Tuhtasin

doi:10.1134/s1995080220060086

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2023

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Cited by 7 publications

(2 citation statements)

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“…The papers [11] and [12] are devoted to investigation of the double-and simple-layer potentials for a three-dimensional singular elliptic equation of the form…”

Section: Introductionmentioning

confidence: 99%

On Potential Theory for the Generalized Bi-Axially Symmetric Elliptic Equation in the Plane

Ergashev

Hasanov

2021

JMMCS

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“…The papers [11] and [12] are devoted to investigation of the double-and simple-layer potentials for a three-dimensional singular elliptic equation of the form…”

Section: Introductionmentioning

confidence: 99%

On Potential Theory for the Generalized Bi-Axially Symmetric Elliptic Equation in the Plane

Ergashev

Hasanov

2021

JMMCS

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“…In a recent paper [5], the generalized Holmgren problem for equation (2) in some part of the first hyperoctant of the ball (in the finite domain) is written out in an explicit form and in case m = 3 and n = 1 the potential theory in the domain bounded in a half-space is constructed [6].…”

Section: Introductionmentioning

confidence: 99%

Lauricella hypergeometric function and its application to the solution of the Neumann problem for a multidimensional elliptic equation with several singular coefficients in an infinite domain

Ergashev,

Tulakova

2021

Preprint

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At present, the fundamental solutions of the multidimensional elliptic equation with the several singular coefficients are known and they are expressed in terms of the Lauricella hypergeometric function of many variables. In this paper we study the Neumann problem for a multidimensional elliptic equation with several singular coefficients in the infinite domain. Using the method of the integral energy the uniqueness of solution has been proved. In the course of proving the existence of the explicit solution of the Neumann problem, a differentiation formula, some adjacent and limiting relations for the Lauricella hypergeometric functions and the values of some multidimensional improper integrals are used.

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Exact Solutions of the Thin Beam with Degrading Hysteresis Behavior

Hasanov

Djuraev

2021

Lobachevskii J Math

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Potentials for Three-Dimensional Singular Elliptic Equation and Their Application to the Solving a Mixed Problem

Cited by 7 publications

References 9 publications

On Potential Theory for the Generalized Bi-Axially Symmetric Elliptic Equation in the Plane

On Potential Theory for the Generalized Bi-Axially Symmetric Elliptic Equation in the Plane

Lauricella hypergeometric function and its application to the solution of the Neumann problem for a multidimensional elliptic equation with several singular coefficients in an infinite domain

Exact Solutions of the Thin Beam with Degrading Hysteresis Behavior

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