A hypersingular integral equation for the floating body problem

Abstract

A new boundary integral equation formulation for the floating body problem, which is defined on a bounded domain and includes a hypersingular and a nonlocal part, is proved to satisfy a Gärding inequality. Under the assunlption of uniqueness it is shown, that an approximating sequence of related semidiscrete integral operators is uniformly bounded invertible.

Keywords:

• Floating body problem
• hypersingular integral equation
• Gárding inequality.

AMS:

• 76B20
• 45A05
• 45M10

^*The work of the author has been supported by the Deutsche Forschungsgerneinschaft (DFG) under Grant Do 2831/2-2 and Ho 1846/1-1.

^*The work of the author has been supported by the Deutsche Forschungsgerneinschaft (DFG) under Grant Do 2831/2-2 and Ho 1846/1-1.

Notes

^*The work of the author has been supported by the Deutsche Forschungsgerneinschaft (DFG) under Grant Do 2831/2-2 and Ho 1846/1-1.