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Potential Analysis

, Volume 38, Issue 4, pp 1123–1171 | Cite as

Nonlinear Neumann–Transmission Problems for Stokes and Brinkman Equations on Euclidean Lipschitz Domains

  • Mirela KohrEmail author
  • Massimo Lanza de Cristoforis
  • Wolfgang L. Wendland
Article

Abstract

The purpose of this paper is to use a layer potential analysis and the Leray–Schauder degree theory to show an existence result for a nonlinear Neumann–transmission problem corresponding to the Stokes and Brinkman operators on Euclidean Lipschitz domains with boundary data in L p spaces, Sobolev spaces, and also in Besov spaces.

Keywords

Stokes and Brinkman operators Lipschitz domain Nonlinear boundary value problem Layer potential operators 

Mathematics Subject Classifications (2010)

35J25 42B20 46E35 76D 76M 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Mirela Kohr
    • 1
    Email author
  • Massimo Lanza de Cristoforis
    • 2
  • Wolfgang L. Wendland
    • 3
  1. 1.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania
  2. 2.Dipartimento di MatematicaUniversità di PadovaPadovaItaly
  3. 3.Institut für Angewandte Analysis und Numerische SimulationUniversität StuttgartStuttgartGermany

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