Justification of the model of cracks of zero width for the Dirichlet problem (Q913146)

The author considers the Laplace operator in a domain in \({\mathbb{R}}^ n\) with a smooth boundary and with boundary conditions of the form \((\partial u/\partial n-\sigma u)|_{\partial \Omega}=0,\) where u is smooth in \(\partial \Omega\) and \(u(x_ 0)=0\) at some \(x_ 0\in \partial \Omega\) fixed. The domain of a suitable selfadjoint extension is studied. The asymptotic of the Green functions \(G_{\sigma}(x,y;k)\) as \(\sigma\) \(\to \infty\) is investigated.