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Approximation of point interactions by geometric perturbations in two-dimensional domains
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SYSNO ASEP 0560991 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Approximation of point interactions by geometric perturbations in two-dimensional domains Author(s) Borisov, D. I. (CZ)
Exner, Pavel (UJF-V) RID, ORCID, SAINumber of authors 2 Article number 2250003 Source Title Bulletin of Mathematical Sciences - ISSN 1664-3607
Roč. 13, č. 2 (2023)Number of pages 30 s. Publication form Print - P Language eng - English Country SG - Singapore Keywords Singular Schrodinger operator ; point interaction ; norm resolvent convergence ; small hole ; Robin condition OECD category Pure mathematics R&D Projects GA21-07129S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support UJF-V - RVO:61389005 UT WOS 000848580300001 EID SCOPUS 85136095427 DOI 10.1142/S1664360722500035 Annotation In this paper, 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 that 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2024 Electronic address https://doi.org/10.1142/S1664360722500035
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