Approximation of point interactions by geometric perturbations in two-dimensional domains
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00560991" target="_blank" >RIV/61389005:_____/23:00560991 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/23:00364187 RIV/62690094:18470/23:50019583
Result on the web
<a href="https://doi.org/10.1142/S1664360722500035" target="_blank" >https://doi.org/10.1142/S1664360722500035</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S1664360722500035" target="_blank" >10.1142/S1664360722500035</a>
Alternative languages
Result language
angličtina
Original language name
Approximation of point interactions by geometric perturbations in two-dimensional domains
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Bulletin of Mathematical Sciences
ISSN
1664-3607
e-ISSN
1664-3615
Volume of the periodical
13
Issue of the periodical within the volume
2
Country of publishing house
SG - SINGAPORE
Number of pages
30
Pages from-to
2250003
UT code for WoS article
000848580300001
EID of the result in the Scopus database
2-s2.0-85136095427