Spectral Convergence of Neumann Laplacian Perturbed by an Infinite Set of Curved Holes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F24%3AA2502MTQ" target="_blank" >RIV/61988987:17310/24:A2502MTQ - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10231-023-01414-y" target="_blank" >https://link.springer.com/article/10.1007/s10231-023-01414-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10231-023-01414-y" target="_blank" >10.1007/s10231-023-01414-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Spectral Convergence of Neumann Laplacian Perturbed by an Infinite Set of Curved Holes

Popis výsledku v původním jazyce

We propose the novel spectral properties of the Neumann Laplacian in a two-dimensional bounded domain perturbed by an infinite number of compact sets with zero Lebesgue measure, so-called curved holes. These holes consist of segments or parts of curves enclosed in small spheres such that the diameters of holes tend to zero as the number of holes approaches infinity. Specifically, we rigorously demonstrate that the spectrum of the Neumann Laplacian on the perturbed domain converges to that of the original operator on the domain without holes under specific geometric assumptions and an appropriate selection of hole sizes. Furthermore, we derive sophisticated estimates on the convergence rate in terms of operator norms and estimate the Hausdorff distance between the spectra of the Laplacians

Název v anglickém jazyce

Spectral Convergence of Neumann Laplacian Perturbed by an Infinite Set of Curved Holes

Popis výsledku anglicky

We propose the novel spectral properties of the Neumann Laplacian in a two-dimensional bounded domain perturbed by an infinite number of compact sets with zero Lebesgue measure, so-called curved holes. These holes consist of segments or parts of curves enclosed in small spheres such that the diameters of holes tend to zero as the number of holes approaches infinity. Specifically, we rigorously demonstrate that the spectrum of the Neumann Laplacian on the perturbed domain converges to that of the original operator on the domain without holes under specific geometric assumptions and an appropriate selection of hole sizes. Furthermore, we derive sophisticated estimates on the convergence rate in terms of operator norms and estimate the Hausdorff distance between the spectra of the Laplacians

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Annali di Matematica Pura ed Applicata (1923)

ISSN

0373-3114

e-ISSN

1618-1891

Svazek periodika

—

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

17

Strana od-do

1569-1585

Kód UT WoS článku

001136073600001

EID výsledku v databázi Scopus

2-s2.0-85181506779