On the Helmholtz decomposition in general unbounded domains

Reinhard Farwig, Hideo Kozono, Hermann Sohr

Research output: Contribution to journalArticle

32 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)239-248
Number of pages10
JournalArchiv der Mathematik
Volume88
Issue number3
DOIs
Publication statusPublished - 2007 Mar
Externally publishedYes

Fingerprint

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

Keywords

  • General unbounded domains
  • Helmholtz decomposition
  • Sum and intersection spaces

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Archiv der Mathematik, Vol. 88, No. 3, 03.2007, p. 239-248.

Research output: Contribution to journalArticle

Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann. / On the Helmholtz decomposition in general unbounded domains. In: Archiv der Mathematik. 2007 ; Vol. 88, No. 3. pp. 239-248.
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