Stability of mappings with bounded distortion in the Sobolev norm on the John domains of Heisenberg groups |
| |
Authors: | D V Isangulova |
| |
Institution: | (1) Sobolev Institute of Mathematics, Novosibirsk, Russia |
| |
Abstract: | This article completes the authors’s series on stability in the Liouville theorem on the Heisenberg group. We show that every mapping with bounded distortion on a John domain of the Heisenberg group is approximated by a conformal mapping with order of closeness √K ? 1 in the uniform norm and with order of closeness K ? 1 in the Sobolev L p 1 -norm for all p < C/K?1. We construct two examples, demonstrating the asymptotic sharpness of our results. |
| |
Keywords: | Heisenberg group mapping with bounded distortion John domain M?bius transformation |
本文献已被 SpringerLink 等数据库收录! |