Application to cylindrical boundary value problems

  • Tobias Nau


In this chapter the Fourier transform approach and the Fourier series approach from the previous chapters are employed to investigate cylindrical boundary value problems. With their aid, a model problem for cylindrical boundary value problems containing partially non-constant coefficients can be treated. Thanks to R-bounds derived for the solution operator of the model problem a localization procedure as known for problems in the whole space can be carried out to deal with fully non-constant coefficients. The crucial assumption is that the cylindrical boundary value problem is parameter-elliptic. As a main result, we prove pseudo-R-sectoriality of the according L p -realizations. Due to the results from Chapter 5 this implies results on the associated parabolic problems. At the end of the chapter we focus on the Laplacian subject to mixed periodic and Dirichlet-Neumann boundary conditions in cylindrical domains.


Neumann Boundary Condition Open Covering Lipschitz Domain Exterior Domain Observation Window 
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Copyright information

© Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden 2012

Authors and Affiliations

  • Tobias Nau
    • 1
  1. 1.KonstanzGermany

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