On fundamental solutions for 3D singular elliptic equations with a parameter

DOI10.1016/J.AML.2010.10.013zbMath1205.35128OpenAlexW1976616675MaRDI QIDQ619828

Sumit K. Garg

Publication date: 18 January 2011

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2010.10.013

zbMATH Keywords

Laplace equationAppel's hypergeometric functionsHorn's hypergeometric functionsLauricella's hypergeometric functionssingular elliptic equation with parameter

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Other basic hypergeometric functions and integrals in several variables (33D70) Singular elliptic equations (35J75)

Related Items (9)

CONFLUENT HYPERGEOMETRIC FUNCTIONS OF MANY VARIABLES AND THEIR APPLICATION TO THE FINDING OF FUNDAMENTAL SOLUTIONS OF THE GENERALIZED HELMHOLTZ EQUATION WITH SINGULAR COEFFICIENTS ⋮ DIRICHLET PROBLEM FOR THE MULTUDIMENSIONAL HELMHOLTZ EQUATION WITH ONE SINGULAR COEFFICIENT ⋮ On fundamental solutions for multidimensional Helmholtz equation with three singular coefficients ⋮ Potentials for three-dimensional singular elliptic equation and their application to the solving a mixed problem ⋮ Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables ⋮ The Dirichlet problem for a 3D elliptic equation with two singular coefficients ⋮ Потенциалы для трехмерного эллиптического уравнения с одним сингулярным коэффициентом и их применение ⋮ Fundamental Solutions for a Class of Multidimensional Elliptic Equations with Several Singular Coefficients ⋮ Spatial boundary problem with the Dirichlet-Neumann condition for a singular elliptic equation

Cites Work

• Fundamental solutions for a class of three-dimensional elliptic equations with singular coefficients
• A problem for the linearized Boussinesq equation with a nonlocal Samarskii condition
• A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain
• Fundamental solutions for the Tricomi operator
• Decomposition formulas associated with the Lauricella multivariable hypergeometric functions
• Some decomposition formulas associated with the Lauricella function \(F_{A}^{(r)}\) and other multiple hypergeometric functions
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