Regularity of Solutions of the Weak Floating Beam Problem

  • Karl Doppel

    Freie Universität Berlin, Germany
  • Bernd Schomburg

    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 H2H^2-space in the neighbourhood of the endpoints of the beam.

Cite this article

Karl Doppel, Bernd Schomburg, Regularity of Solutions of the Weak Floating Beam Problem. Z. Anal. Anwend. 10 (1991), no. 4, pp. 461–477

DOI 10.4171/ZAA/468