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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21340/23:00364187 RIV/62690094:18470/23:50019583

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Bulletin of Mathematical Sciences

ISSN

1664-3607

e-ISSN

1664-3615

Svazek periodika

13

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

30

Strana od-do

2250003

Kód UT WoS článku

000848580300001

EID výsledku v databázi Scopus

2-s2.0-85136095427