Laplace operator with \(\delta\)-like potentials
type: Item
instance of: scholarly article
title: Laplace operator with \(\delta\)-like potentials
zbMATH Open document ID: 1304.35236
DOI: 10.3103/S1066369X14020029
author: N. E. Tokmagambetov
author: B. E. Kanguzhin
author: D. B. Nurakhmetov
published in: Russian Mathematics
publication date: 2014-11-05T00:00:00Z
review text: Let \(\Omega \) be a simply connected domain with smooth boundary in \(\mathbb R^2\), and \(M=[x_0,y_0]\) be a fixed inner point of the domain \(\Omega \). Denote \(\Omega_0 =\Omega \setminus \{ M\} \). Denote by \(G(x,y,x_0,y_0)\) the Green function of the Dirichlet problem for the Laplace equation corresponding to \(\Omega \) and \([x_0,y_0]\). The Laplace operator is studied on the space \(\{ h(x,y)=h_1(x,y)+\alpha G(x,y,x_0,y_0);\alpha \in\mathbb R, h_1\in W^{2,2}(\Omega ), h_1 =0\) on \(\partial \Omega \} \). An analog of the Green formula is obtained.
reviewed by: Dagmar Medková
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J08
zbMATH DE Number: 6366137
zbMATH Keywords: Laplace operator
zbMATH Keywords: punctured domain
zbMATH Keywords: Green formula
zbMATH Keywords: self-adjoint extension
zbMATH Keywords: well-posed problem
MaRDI profile type: Publication
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full work available at URL: s1066369x14020029
OpenAlex ID: W1970700979
description: scientific article; zbMATH DE number 6366137