Application to cylindrical boundary value problems
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.
KeywordsNeumann Boundary Condition Open Covering Lipschitz Domain Exterior Domain Observation Window
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