Discrete Fourier multipliers and cylindrical boundary value problems
R. Denk and Tobias Nau
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.
Published in Proc. Roy. Soc. Edinburgh Sect. A 143 (2013), 1163–1183.
The paper is available here (Final version).