The \bar{\partial}_b Neumann problem on noncharacteristic domains
| dc.creator | Hladky, Robert K. | |
| dc.date | 2008-03-03 | |
| dc.date.accessioned | 2026-07-07T09:24:31Z | |
| dc.date.available | 2026-07-07T09:24:31Z | |
| dc.description | We study the $\bar{\partial}_b$-Neumann problem for domains $Ω$ contained in a strictly pseudoconvex manifold M^{2n+1} whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts of a single CR function w. When the Kohn Laplacian is a priori known to have closed range in L^2, we prove sharp regularity and estimates for solutions. We establish a condition on the boundary which is sufficient for the Kohn Laplacian to be Fredholm on $L^2_{(0,q)}(Ω)$ and show that this condition always holds when M is embedded as a hypersurface in C^{n+1}. We present examples where the inhomogeneous $\bar{\partial}_b$ equation can always be solved smoothly up to the boundary on (p,q)-forms with 0<q<n-1. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/0803.0336 | |
| dc.identifier | http://arxiv.org/abs/0803.0336 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156120 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 32W10; 32V20; 35H20 | |
| dc.title | The \bar{\partial}_b Neumann problem on noncharacteristic domains | |
| dc.type | text |