Nonlinear nonhomogeneous Neumann problem on the Heisenberg group

2020 ◽  
pp. 1-14 ◽  
Author(s):  
F. Sarafi ◽  
A. Razani
Keyword(s):  
Heisenberg Group ◽  
Neumann Problem

The Explicit Solution of the -Neumann Problem in a Non-Isotropic Siegel Domain

1997 ◽  
Vol 49 (6) ◽  
pp. 1299-1322 ◽  
Author(s):  
Jingzhi Tie
Keyword(s):  
Differential Equation ◽  
Fundamental Solution ◽  
Heat Equation ◽  
Heisenberg Group ◽  
Neumann Problem ◽  
Explicit Solution ◽  
Laplacian Operator ◽  
Siegel Domain ◽  
The Neumann Problem ◽  
Image Position

AbstractIn this paper, we solve the-Neumann problem on (0, q) forms, 0 ≤ q ≤ n, in the strictly pseudoconvex non-isotropic Siegel domain:where aj> 0 for j = 1,2, . . . , n. The metric we use is invariant under the action of the Heisenberg group on the domain. The fundamental solution of the related differential equation is derived via the Laguerre calculus. We obtain an explicit formula for the kernel of the Neumann operator. We also construct the solution of the corresponding heat equation and the fundamental solution of the Laplacian operator on the Heisenberg group.

The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group ℍ n $\mathbb H_{n}$

2016 ◽  
Vol 45 (1) ◽  
pp. 119-133 ◽  
Author(s):  
Shivani Dubey ◽  
Ajay Kumar ◽  
Mukund Madhav Mishra
Keyword(s):  
Heisenberg Group ◽  
Neumann Problem ◽  
Kohn Laplacian ◽  
The Neumann Problem

Weighted estimates for commutators of Hausdorff operators on the Heisenberg group

2020 ◽  
pp. 39-62
Author(s):  
Nguyen Minh Chuong ◽  
◽  
Dao Van Duong ◽  
Nguyen Duc Duyet ◽  
◽  
...  
Keyword(s):  
Heisenberg Group ◽  
Weighted Estimates ◽  
Hausdorff Operators

The horofunction boundary of the Heisenberg group

2009 ◽  
Vol 242 (2) ◽  
pp. 299-310 ◽  
Author(s):  
Tom Klein ◽  
Andrew Nicas
Keyword(s):  
Heisenberg Group
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