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Justification of the model of cracks of zero width for the Dirichlet problem. (English. Russian original) Zbl 0699.35231

Sib. Math. J. 30, No. 3, 428-432 (1989); translation from Sib. Mat. Zh. 30, No. 3(175), 103-108 (1989).
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.
Reviewer: G.Popov

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
78A45 Diffraction, scattering
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References:

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