Spectral Convergence of Neumann Laplacian Perturbed by an Infinite Set of Curved Holes
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Spectral Convergence of Neumann Laplacian Perturbed by an Infinite Set of Curved Holes
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annali di Matematica Pura ed Applicata (1923)
ISSN
0373-3114
e-ISSN
1618-1891
Volume of the periodical
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Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
17
Pages from-to
1569-1585
UT code for WoS article
001136073600001
EID of the result in the Scopus database
2-s2.0-85181506779