Operator estimates for the Neumann sieve problem
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00570282" target="_blank" >RIV/61389005:_____/23:00570282 - isvavai.cz</a>
Alternative codes found
RIV/62690094:18470/23:50020247
Result on the web
<a href="https://doi.org/10.1007/s10231-023-01308-z" target="_blank" >https://doi.org/10.1007/s10231-023-01308-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10231-023-01308-z" target="_blank" >10.1007/s10231-023-01308-z</a>
Alternative languages
Result language
angličtina
Original language name
Operator estimates for the Neumann sieve problem
Original language description
Let omega be a domain in R-n, gamma be a hyperplane intersecting omega, epsilon > 0 be a small parameter, and D-k,D-epsilon,D- k = 1, 2, 3 ... be a family of small holes in gamma n omega, when is an element of -> 0, the number of holes tends to infinity, while their diameters tends to zero. Let AE be the Neumann Laplacian in the perforated domain omega(epsilon) = omega gamma(epsilon), where gamma(epsilon) = gamma (UkDk,epsilon) ('sieve'). It is well-known that if the sizes of holes are carefully chosen, A(epsilon) converges in the strong resolvent sense to the Laplacian on omega gamma subject to the so-called delta'-conditions on gamma & cap, omega. In the current work we improve this result: under rather general assumptions on the shapes and locations of the holes we derive estimates on the rate of convergence in terms of L-2 L-2 and L-2 -> H-1 operator norms. In the latter case a special corrector is required.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA22-18739S" target="_blank" >GA22-18739S: Asymptotic and spectral analysis of operators in mathematical physics</a><br>
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
Annali di Matematica Pura ed Applicata
ISSN
0373-3114
e-ISSN
1618-1891
Volume of the periodical
202
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
36
Pages from-to
1955-1990
UT code for WoS article
000934589900002
EID of the result in the Scopus database
2-s2.0-85147753214