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Maximal Regularity of the Stokes Operator in General Unbounded Domains of ℝ n

In: Functional Analysis and Evolution Equations

Author

Listed:
  • Reinhard Farwig

    (Technische Universität Darmstadt, Fachbereich Mathematik)

  • Hideo Kozono

    (Tôhoku University, Mathematical Institute)

  • Hermann Sohr

    (Universität Paderborn, Fakultät für Elektrotechnik Informatik und Mathematik)

Abstract

It is well known that the Helmholtz decomposition of L q -spaces fails to exist for certain unbounded smooth domains unless q ≠ 2. Hence also the Stokes operator and the Stokes semigroup are not well defined for these domains when q ≠ 2. In this note, we generalize a new approach to the Stokes operator in general unbounded domains from the three-dimensional case, see [6], to the n-dimensional one, n ≥ 2, by replacing the space L q , 1 0, for every unbounded domain of uniform C 1,1-type in ℝ n .

Suggested Citation

  • Reinhard Farwig & Hideo Kozono & Hermann Sohr, 2007. "Maximal Regularity of the Stokes Operator in General Unbounded Domains of ℝ n," Springer Books, in: Herbert Amann & Wolfgang Arendt & Matthias Hieber & Frank M. Neubrander & Serge Nicaise & Joachim vo (ed.), Functional Analysis and Evolution Equations, pages 257-272, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7794-6_17
    DOI: 10.1007/978-3-7643-7794-6_17
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