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Newtonian and Single Layer Potentials for the Stokes System with L Coefficients and the Exterior Dirichlet Problem

  • Mirela Kohr
  • Sergey E. Mikhailov
  • Wolfgang L. WendlandEmail author
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

A mixed variational formulation of some problems in L2-based Sobolev spaces is used to define the Newtonian and layer potentials for the Stokes system with L coefficients on Lipschitz domains in \({\mathbb R}^3\). Then the solution of the exterior Dirichlet problem for the Stokes system with L coefficients is presented in terms of these potentials and the inverse of the corresponding single layer operator.

Keywords

Stokes system with L coefficients Newtonian and layer potentials Variational approach Inf-sup condition Sobolev spaces 

Mathematics Subject Classification (2010)

Primary 35J25 35Q35 42B20 46E35 Secondary 76D 76M 

Notes

Acknowledgements

The research has been supported by the grant EP/M013545/1: “Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs” from the EPSRC, UK. Part of this work was done in April/May 2018, when M. Kohr visited the Department of Mathematics of the University of Toronto. She is grateful to the members of this department for their hospitality.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mirela Kohr
    • 1
  • Sergey E. Mikhailov
    • 2
  • Wolfgang L. Wendland
    • 3
    Email author
  1. 1.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania
  2. 2.Department of MathematicsBrunel University LondonUxbridgeUK
  3. 3.Institut für Angewandte Analysis und Numerische SimulationUniversität StuttgartStuttgartGermany

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