Operator Estimates in Two-Dimensional Problems with a Frequent Alternation in the Case of Small Parts with the Dirichlet Condition
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50021095" target="_blank" >RIV/62690094:18470/23:50021095 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1134/S0081543823030057" target="_blank" >https://doi.org/10.1134/S0081543823030057</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1134/S0081543823030057" target="_blank" >10.1134/S0081543823030057</a>
Alternative languages
Result language
angličtina
Original language name
Operator Estimates in Two-Dimensional Problems with a Frequent Alternation in the Case of Small Parts with the Dirichlet Condition
Original language description
A two-dimensional boundary value problem is studied for a general scalar elliptic second-order equation of the general form with frequent alternation of boundary conditions. The alternation is defined on small, closely spaced parts of the boundary on which the Dirichlet boundary condition and the nonlinear Robin boundary condition are set alternately. The distribution and size of these segments are arbitrary. The case is considered when, upon homogenization, the Dirichlet boundary condition completely disappears and only the original nonlinear Robin boundary condition remains. The main result is estimates for the W-2(1)- and L-2-norms of the difference between the solutions of the perturbed and homogenized problems, which are uniform in the L-2-normof the right-hand side and characterize the rate of convergence. It is shown that these estimates are order sharp.
Czech name
—
Czech description
—
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
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
Proceedings of the Steklov Institute of Mathematics
ISSN
0081-5438
e-ISSN
1531-8605
Volume of the periodical
321
Issue of the periodical within the volume
SUPPL 1
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
"S33"-"S52"
UT code for WoS article
001073881600004
EID of the result in the Scopus database
2-s2.0-85171379977