On the Helmholtz decomposition in general unbounded domains |
| |
Authors: | Reinhard Farwig Hideo Kozono Hermann Sohr |
| |
Institution: | 1.Fachbereich Mathematik,Technische Universit?t Darmstadt,Darmstadt,Germany;2.Mathematical Institute,Tohoku University,Sendai,Japan;3.Fakult?t für Elektrotechnik,Informatik und Mathematik Universit?t Paderborn,Paderborn,Germany |
| |
Abstract: | It is well known that the Helmholtz decomposition of Lq-spaces fails to exist for certain unbounded smooth planar domains unless q = 2, see 2], 9]. As recently shown 6], the Helmholtz projection does exist for general unbounded domains of uniform C2-type in
if we replace the space Lq, 1 < q < ∞, by L2 ∩ Lq for q > 2 and by Lq + L2 for 1 < q < 2. In this paper, we generalize this new approach from the three-dimensional case to the n-dimensional case, n ≥ 2. By these means it is possible to define the Stokes operator in arbitrary unbounded domains of uniform
C2-type.
Received: 15 February 2006 |
| |
Keywords: | 35Q35 35Q30 76D07 |
本文献已被 SpringerLink 等数据库收录! |
|