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Zeitschrift für Analysis und ihre Anwendungen

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Volume 10, Issue 4, 1991, pp. 461–477
DOI: 10.4171/ZAA/468

Published online: 1991-12-31

Regularity of Solutions of the Weak Floating Beam Problem

Karl Doppel[1] and Bernd Schomburg[2]

(1) Freie Universität Berlin, Germany
(2) Freie Universität Berlin, Germany

This paper describes a weak formulation of the time-harmonic two-dimensional floating beam problem in a fluid domain of finite depth. This is a simplified version of the floating body problem which was investigated by F. John in his classic papers [9,10] in 1950. Contrary to the integral equation approach of F. John we use a Hilbert-space method based on the investigation of a not necessarily positive definite sesquilinear form. Interior as well as boundary regularity are the main concernsof this paper. Especially we show that the solutions lie in a weighted $H^2$-space in the neighbourhood of the endpoints of the beam.

Keywords: Weighted regularity, floating beam problem

Doppel Karl, Schomburg Bernd: Regularity of Solutions of the Weak Floating Beam Problem. Z. Anal. Anwend. 10 (1991), 461-477. doi: 10.4171/ZAA/468