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Application to cylindrical boundary value problems

In: Lp-Theory of Cylindrical Boundary Value Problems

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  • Tobias Nau

Abstract

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.

Suggested Citation

  • Tobias Nau, 2012. "Application to cylindrical boundary value problems," Springer Books, in: Lp-Theory of Cylindrical Boundary Value Problems, chapter 8, pages 99-132, Springer.
    • Handle: RePEc:spr:sprchp:978-3-8348-2505-6_8
    DOI: 10.1007/978-3-8348-2505-6_8
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