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

Reinhard Farwig (), Hideo Kozono () and Hermann Sohr ()
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Reinhard Farwig: Technische Universität Darmstadt, Fachbereich Mathematik
Hideo Kozono: Tôhoku University, Mathematical Institute
Hermann Sohr: Universität Paderborn, Fakultät für Elektrotechnik Informatik und Mathematik

A chapter in Functional Analysis and Evolution Equations, 2007, pp 257-272 from Springer

Abstract: 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 .

Keywords: General unbounded domains; domains of uniform C 1; 1-type; Stokes operator; maximal regularity (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-7643-7794-6_17

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