Approximation of point interactions by geometric perturbations in two-dimensional domains

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-08-02 DOI:10.1142/s1664360722500035

D. Borisov, P. Exner

引用次数: 2

Abstract

We present a new type of approximation of a second-order elliptic operator in a planar domain with a point interaction. It is of a geometric nature, the approximating family consists of operators with the same symbol and regular coefficients on the domain with a small hole. At the boundary of it Robin condition is imposed with the coefficient which depends on the linear size of a hole. We show that as the hole shrinks to a point and the parameter in the boundary condition is scaled in a suitable way, nonlinear and singular, the indicated family converges in the norm-resolvent sense to the operator with the point interaction. This resolvent convergence is established with respect to several operator norms and order-sharp estimates of the convergence rates are provided.

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二维区域中点相互作用的几何摄动近似

给出了具有点相互作用的平面域上二阶椭圆算子的一种新的逼近形式。它是一个几何性质的近似族，由具有相同符号的算子和具有小孔的域上的正则系数组成。在其边界处施加Robin条件，其系数取决于孔的线性尺寸。结果表明，当孔洞缩小到一个点，且边界条件中的参数以适当的方式缩放时，所指示的族在范数解析意义上收敛于具有点相互作用的算子。在若干算子范数下建立了该收敛性，并给出了收敛速率的阶锐估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.