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

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.

scholarly journals The Neumann problem for nonlocal nonlinear diffusion equations

2007 ◽  
Vol 8 (1) ◽  
pp. 189-215 ◽  
Author(s):  
Fuensanta Andreu ◽  
José M. Mazón ◽  
Julio D. Rossi ◽  
Julián Toledo
Keyword(s):  
Neumann Problem ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
The Neumann Problem ◽  
Nonlocal Nonlinear
Sign in / Sign up

Export Citation Format

Share Document