On the Helmholtz decomposition in general unbounded domains

Reinhard Farwig, Hideo Kozono, Hermann Sohr

研究成果: Article

32 引用 (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.

元の言語English
ページ(範囲)239-248
ページ数10
ジャーナルArchiv der Mathematik
88
発行部数3
DOI
出版物ステータスPublished - 2007 3
外部発表Yes

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Helmholtz Decomposition
Unbounded Domain
Stokes Operator
Hermann Von Helmholtz
n-dimensional
Projection
Three-dimensional
Generalise
Arbitrary

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

On the Helmholtz decomposition in general unbounded domains. / Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann.

:: Archiv der Mathematik, 巻 88, 番号 3, 03.2007, p. 239-248.

研究成果: Article

Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann. / On the Helmholtz decomposition in general unbounded domains. :: Archiv der Mathematik. 2007 ; 巻 88, 番号 3. pp. 239-248.
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