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The L p -Helmholtz projection in finite cylinders

Tobias Nau — 2015

Czechoslovak Mathematical Journal

In this article we prove for 1 < p < the existence of the L p -Helmholtz projection in finite cylinders Ω . More precisely, Ω is considered to be given as the Cartesian product of a cube and a bounded domain V having C 1 -boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in Ω is solved, which implies existence and a representation of the L p -Helmholtz projection as...

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