scholarly journals Green’s Function for a Slice of the Korányi Ball in the Heisenberg GroupHn

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Shivani Dubey ◽  
Ajay Kumar ◽  
Mukund Madhav Mishra
Keyword(s):  
Dirichlet Problem ◽  
Heisenberg Group ◽  
Green’S Function ◽  
Green's Function ◽  
Representation Formula ◽  
Radial Symmetry ◽  
The Given ◽  
Explicit Expressions

We give a representation formula for solution of the inhomogeneous Dirichlet problem on the upper half Korányi ball and for the slice of the Korányi ball in the Heisenberg groupHnby obtaining explicit expressions of Green-like kernel when the given data has certain radial symmetry.

Estimates of the Green’s Function and its Regular Part on Heisenberg Group Domains

2011 ◽  
Vol 11 (3) ◽  
Author(s):  
Najoua Gamara ◽  
Habiba Guemri
Keyword(s):  
Heisenberg Group ◽  
Green’S Function ◽  
Green's Function ◽  
Forthcoming Paper ◽  
Regular Part ◽  
Kohn Laplacian ◽  
Preliminary Work ◽  
Characteristic Points ◽  
The Given ◽  
Euclidean Domains

AbstractThis paper is a preliminary work on Heisenberg group domains, devoted to the study of the Green’s function for the Kohn Laplacian on domains far away from the set of characteristic points. We give some estimates of the Green’s function, its regular part and their derivatives analogous to those proved by A. Bahri, Y.Y. Li, O. Rey in [1], and O. Rey in [16] for Euclidean domains. While the study of such functions on the set of characteristic points of the given domain will be discussed in a forthcoming paper.

The Heat Kernel and Green's Function on a Manifold with Heisenberg Group as Boundary

2004 ◽  
Vol 56 (3) ◽  
pp. 590-611
Author(s):  
Yilong Ni
Keyword(s):  
Riemannian Manifold ◽  
Heisenberg Group ◽  
Green’S Function ◽  
Heat Kernel ◽  
Green's Function ◽  
Beltrami Operator ◽  
Small Time ◽  
Time Estimates

AbstractWe study the Riemannian Laplace-Beltrami operator L on a Riemannian manifold with Heisenberg group H1 as boundary. We calculate the heat kernel and Green's function for L, and give global and small time estimates of the heat kernel. A class of hypersurfaces in this manifold can be regarded as approximations of H1. We also restrict L to each hypersurface and calculate the corresponding heat kernel and Green's function. We will see that the heat kernel and Green's function converge to the heat kernel and Green's function on the boundary.

Integral Equation Approach for Computing Green’s Function on Doubly Connected Regions via the Generalized Neumann Kernel

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Siti Zulaiha Aspon ◽  
Ali Hassan Mohamed Murid ◽  
Mohamed M. S. Nasser ◽  
Hamisan Rahmat
Keyword(s):  
Integral Equation ◽  
Dirichlet Problem ◽  
Linear System ◽  
Green’S Function ◽  
Green's Function ◽  
Boundary Integral ◽  
Generalized Neumann Kernel ◽  
Integral Equation Approach ◽  
Gauss Elimination ◽  
Neumann Kernel

This research is about computing the Green’s function on doubly connected regions by using the method of boundary integral equation. The method depends on solving a Dirichlet problem. The Dirichlet problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The method for solving this integral equation is by using the Nystrӧm method with trapezoidal rule to discretize it to a linear system. The linear system is then solved by the Gauss elimination method. Mathematica plots of Green’s functions for several test regions are also presented.

scholarly journals Green’s function for certain domains in the Heisenberg group H n

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Mukund Madhav Mishra ◽  
Ajay Kumar ◽  
Shivani Dubey
Keyword(s):  
Heisenberg Group ◽  
Green’S Function ◽  
Green's Function
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