Regularity of Solutions of the Weak Floating Beam Problem

Abstract

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.