Green's function for Laplace's equation in a circular ring with radiation type boundary conditions

1961 ◽  
Vol 12 (4) ◽  
pp. 322-328 ◽  
Author(s):  
James F. Heyda
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Circular Ring ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Type Boundary ◽  
Radiation Type

On Green’s function for Laplace’s equation in a rigid tube

2021 ◽  
Vol 80 (1) ◽  
pp. 87-98
Author(s):  
P. Martin
Keyword(s):  
Point Source ◽  
Green’S Function ◽  
Potential Theory ◽  
Green's Function ◽  
Classical Problem ◽  
Extensive Literature ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Rigid Tube

A classical problem from potential theory (a point source inside a long rigid tube) is revisited. It has an extensive literature but its resolution is not straightforward: standard approaches lead to divergent integrals or require the discarding of infinite constants. We show that the problem can be solved rigorously using classical methods.

A Liouville Type Theorem for Poly-harmonic System with Dirichlet Boundary Conditions in a Half Space

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Zhao Liu ◽  
Wei Dai
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Dirichlet Boundary ◽  
Type Theorem ◽  
Dirichlet Boundary Conditions ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Harmonic System

AbstractIn this paper, we consider the following poly-harmonic system with Dirichlet boundary conditions in a half space ℝwherewhereis the Green’s function in ℝ

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