On the Helmholtz decomposition in general unbounded domains

• Autores: Reinhard Farwig, Hideo Kozono, Hermann Sohr
• Localización: Archiv der Mathematik, ISSN 0003-889X, Vol. 88, Nº. 3, 2007, págs. 239-248
• Idioma: inglés
• DOI: 10.1007/s00013-006-1910-8
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• Resumen

  • 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 < 8, by L2 n 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