Approximation of point interactions by geometric perturbations in two-dimensional domains
| Autor: | D. I. Borisov, P. Exner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Bulletin of Mathematical Sciences, Vol 13, Iss 02 (2023) |
| Druh dokumentu: | article |
| ISSN: | 16643607 1664-3615 1664-3607 |
| DOI: | 10.1142/S1664360722500035 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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