The heat equation for the $$\bar \partial $$ -neumann problem in a strictly pseudoconvex siegel domain, II-neumann problem in a strictly pseudoconvex siegel domain, II

1981 ◽  
Vol 39 (1) ◽  
pp. 189-202 ◽  
Author(s):  
Nancy K. Stanton
Keyword(s):  
Heat Equation ◽  
Neumann Problem ◽  
Siegel Domain

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 Heat Equation for the -Neumann Problem, I

1987 ◽  
Vol 12 (4) ◽  
pp. 67-112 ◽  
Author(s):  
Richard Beals ◽  
Nancy K. Stanton
Keyword(s):  
Heat Equation ◽  
Neumann Problem ◽  
The Neumann Problem
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