On the Helmholtz decomposition in general unbounded domains

Reinhard Farwig*, Hideo Kozono, Hermann Sohr

*この研究の対応する著者

研究成果: Article査読

41 被引用数 (Scopus)

抄録

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 ℝ3 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.

本文言語English
ページ(範囲)239-248
ページ数10
ジャーナルArchiv der Mathematik
88
3
DOI
出版ステータスPublished - 2007 3 1
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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