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Approximation of point interactions by geometric perturbations in two-dimensional domains.
- Source :
- Bulletin of Mathematical Sciences (World Scientific); Aug2023, Vol. 13 Issue 2, p1-30, 30p
- Publication Year :
- 2023
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16643607
- Volume :
- 13
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Bulletin of Mathematical Sciences (World Scientific)
- Publication Type :
- Academic Journal
- Accession number :
- 173879008
- Full Text :
- https://doi.org/10.1142/S1664360722500035