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Medientyp:
E-Artikel
Titel:
Discrete Fourier multipliers and cylindrical boundary-value problems
Beteiligte:
Denk, Robert;
Nau, Tobias
Erschienen:
Cambridge University Press (CUP), 2013
Erschienen in:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 143 (2013) 6, Seite 1163-1183
Sprache:
Englisch
DOI:
10.1017/s0308210511001454
ISSN:
0308-2105;
1473-7124
Entstehung:
Anmerkungen:
Beschreibung:
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 × V with ν-periodic boundary conditions in the cylindrical directions. We show that, under suitable assumptions on the coefficients, we obtain maximal Lq-regularity for such problems. For symmetric operators such as the Laplacian, related results for mixed Dirichlet-Neumann boundary conditions on (0, 2π)n × V are deduced.