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Discrete Fourier multipliers and cylindrical boundary value problems

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2011

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Zusammenfassung

We consider operator-valued boundary value problems in (0;2π)n with periodic or, more generally, v-periodic boundary conditions. Using the concept of discrete vector-valued Fourier multipliers, we give equivalent conditions for the unique solvability of the boundary value problem. As an application, we study vector-valued parabolic initial boundary value problems in cylindrical domains (0;2π)n x V with v-periodic boundary conditions in the cylindrical directions. We show that under suitable assumptions on the coefficients, we obtain maximal Lq-regularity for such problems.

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Fachgebiet (DDC)
510 Mathematik

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Discrete Fourier multipliers, maximal regularity, bounded cylindrical domains

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ISO 690DENK, Robert, Tobias NAU, 2011. Discrete Fourier multipliers and cylindrical boundary value problems
BibTex
@techreport{Denk2011Discr-12627,
  year={2011},
  series={Konstanzer Schriften in Mathematik},
  title={Discrete Fourier multipliers and cylindrical boundary value problems},
  number={279},
  author={Denk, Robert and Nau, Tobias}
}
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