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arXiv · 1106.2010

Discrete Fourier multipliers and cylindrical boundary value problems

Tobias Nau·Robert Denk
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Abstract

We consider operator-valued boundary value problems in $(0,2π)^n$ with periodic or, more generally, $ν$-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 $(0,2π)^n\times V$ with $ν$-periodic boundary conditions in the cylindrical directions. We show that under suitable assumptions on the coefficients, we obtain maximal $L^q$-regularity for such problems.

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Tobias Nau, Robert Denk. 2011-06-10. Discrete Fourier multipliers and cylindrical boundary value problems. https://doi.org/10.1017/s0308210511001454

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