  We analyze the approximation by radial basis functions of a hypersingular
integral equation on an open surface. In order to accommodate the homogeneous
essential boundary condition along the surface boundary, scaled radial basis
functions on an extended surface and Lagrangian multipliers on the extension
are used. We prove that our method converges quasi-optimally. Approximation
results for scaled radial basis functions indicate that, for highly regular
radial basis functions, the achieved convergence rates are close to the one of
low-order conforming boundary element schemes. Numerical experiments confirm
our conclusions.
