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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 497, Pages 3–6
DOI: https://doi.org/10.31857/S2686954321020028 (Mi danma161) 		 
This article is cited in 11 scientific papers (total in 11 papers)

MATHEMATICS

Increased integrability of the gradient of the solution to the Zaremba problem for the Poisson equation

Yu. A. Alkhutova, G. A. Chechkinbcd

a Vladimir State University, Vladimir, Russia
b Lomonosov Moscow State University, Moscow, Russia
c Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Science, Ufa, Bashkortostan, Russia
d Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
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DOI: https://doi.org/10.31857/S2686954321020028
Abstract: An estimate is obtained for the increased integrability of the gradient of the solution to the Zaremba problem in a bounded plane domain with a Lipschitz boundary and rapidly alternating Dirichlet and Neumann boundary conditions, with an increased integrability exponent independent of the frequency of the boundary condition change.
Keywords: Meyers estimates, embedding theorems, rapidly changing type of boundary conditions.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00184
Russian Science Foundation 20-11-20272
Alkhutov acknowledges the support of the Russian Foundation for Basic Research (project no. 19-01-00184), and Chechkin acknowledges the support of the Russian Science Foundation (project no. 20-11-20272).
Presented: V. V. Kozlov
Received: 18.02.2021
Revised: 18.02.2021
Accepted: 24.02.2021
English version:
Doklady Mathematics, 2021, Volume 103, Issue 2, Pages 69–71
DOI: https://doi.org/10.1134/S1064562421020022
Bibliographic databases:
Document Type: Article
UDC: 517.954; 517.982
Language: Russian
Citation: Yu. A. Alkhutov, G. A. Chechkin, “Increased integrability of the gradient of the solution to the Zaremba problem for the Poisson equation”, Dokl. RAN. Math. Inf. Proc. Upr., 497 (2021), 3–6; Dokl. Math., 103:2 (2021), 69–71
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
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