The Dirichlet Problem for an Elliptic Equation with Singular Coefficients in a Semi-Cylindrical Domain

2020 ◽  
Vol 41 (9) ◽  
pp. 1898-1909
Author(s):  
A. K. Urinov ◽  
K. T. Karimov
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Cylindrical Domain ◽  
Singular Coefficients

A MIXED PROBLEM FOR A DEGENERATE MULTIDIMENSIONAL ELLIPTIC EQUATION

2021 ◽  
pp. 37-41
Author(s):  
Aisulu K. Tanirbergen
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Classical Solution ◽  
Mixed Problem ◽  
Unique Solvability ◽  
Complex Variable ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Cylindrical Domain

This article shows the unique solvability and obtains an explicit form of the classical solution of the mixed prob-lem in a cylindrical domain for a model degenerate multidimensional elliptic equation. The correctness of boundary value problems in the plane for elliptic equations by the method of the theory of ana-lytic functions of a complex variable has been well studied. The first boundary value problem or the Dirichlet problem for multidimensional elliptic equations with degeneration on the boundary has been sufficiently analyzed. However, as we know, the mixed problem for the indicated equations has been studied very little.

scholarly journals The Dirichlet problem for elliptic equation with several singular coefficients

2018 ◽  
Vol 1 (1) ◽  
pp. 81-99 ◽  
Author(s):  
Tuhtasin G. Ergashev
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Hypergeometric Function ◽  
Unique Solution ◽  
Explicit Form ◽  
Fundamental Solutions ◽  
Singular Elliptic Equation ◽  
Singular Coefficients

AbstractRecently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the Dirichlet problem for an elliptic equation with several singular coefficients in explicit form. When finding a solution, we use decomposition formulas and some adjacent relations for the Lauricella hypergeometric function in many variables.

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