Homogenization for operators with arbitrary perturbations in coefficients
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50021094" target="_blank" >RIV/62690094:18470/23:50021094 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jde.2023.05.048" target="_blank" >https://doi.org/10.1016/j.jde.2023.05.048</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2023.05.048" target="_blank" >10.1016/j.jde.2023.05.048</a>
Alternative languages
Result language
angličtina
Original language name
Homogenization for operators with arbitrary perturbations in coefficients
Original language description
We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. We perturbed it by a first order differential operator arbitrarily depending on a small multi-dimensional parameter and we study the existence of a limiting (homogenized) operator in the sense of the norm resolvent convergence. The first part of our main results states that the norm resolvent convergence is equivalent to the convergence of the coefficients in the perturbing operator in certain space of multipliers. The second part of our results says that the convergence in the mentioned spaces of multipliers is equivalent to the convergence of certain local mean values over small pieces of the considered domains. These results are supported by series of examples. We also provide a series of ways of generating new non-periodically oscillating perturbations for which our results are applicable.& COPY; 2023 Elsevier Inc. All reserved.
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
Journal of differential equations
ISSN
0022-0396
e-ISSN
1090-2732
Volume of the periodical
369
Issue of the periodical within the volume
October
Country of publishing house
US - UNITED STATES
Number of pages
53
Pages from-to
41-93
UT code for WoS article
001024726500001
EID of the result in the Scopus database
2-s2.0-85161645642