Discrete Fourier multipliers and cylindrical boundary value problems

Denk, Robert; Nau, Tobias

Discrete Fourier multipliers and cylindrical boundary value problems

Files

279Denk.pdf(567.66 KB)

Date

2011

Authors

Denk, Robert

Nau, Tobias

Series

Konstanzer Schriften in Mathematik; 279

Publication type

Working Paper/Technical Report

Abstract

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.

Subject (DDC)

510 Mathematics

Keywords

Discrete Fourier multipliers,maximal regularity,bounded cylindrical domains

Cite This

ISO 690

DENK, 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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Yes