Green functions and related boundary value problems on the Heisenberg group
Ajay Kumar, Mukund Madhav Mishra · Complex Variables and Elliptic Equations · 2012
In this article, a modified Kelvin transform on ℍ n using inversion with respect to a ball of arbitrary radius is defined, which gives explicit expressions for Green's function and Poisson's kernel for the Korányi ball of arbitrary radius and annular domain. The solution of the Dirichlet problem for the union of two balls is discussed using the Schwarz's alternating method.