Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50020477" target="_blank" >RIV/62690094:18470/23:50020477 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s13324-022-00765-8" target="_blank" >https://link.springer.com/article/10.1007/s13324-022-00765-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13324-022-00765-8" target="_blank" >10.1007/s13324-022-00765-8</a>
Alternative languages
Result language
angličtina
Original language name
Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit
Original language description
We consider a general second order linear elliptic equation in a finely perforated domain. The shapes of cavities and their distribution in the domain are arbitrary and non-periodic; they are supposed to satisfy minimal natural geometric conditions. On the boundaries of the cavities we impose either the Dirichlet or a nonlinear Robin condition; the choice of the type of the boundary condition for each cavity is arbitrary. Then we suppose that for some cavities the nonlinear Robin condition is sign-definite in certain sense. Provided such cavities and ones with the Dirichlet condition are distributed rather densely in the domain and the characteristic sizes of the cavities and the minimal distances between the cavities satisfy certain simple condition, we show that a solution to our problem tends to zero as the perforation becomes finer. Our main result are order sharp estimates for the L-2- and W-2(1)-norms of the solution uniform in the L-2-norm of the right hand side in the equation.
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
<a href="/en/project/GA22-18739S" target="_blank" >GA22-18739S: Asymptotic and spectral analysis of operators in mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
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
Analysis and Mathematical Physics
ISSN
1664-2368
e-ISSN
1664-235X
Volume of the periodical
13
Issue of the periodical within the volume
1
Country of publishing house
CH - SWITZERLAND
Number of pages
34
Pages from-to
"Article Number: 5"
UT code for WoS article
000889746200001
EID of the result in the Scopus database
2-s2.0-85142723111