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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 512, Pages 47–51
DOI: https://doi.org/10.31857/S268695432260046X (Mi danma397) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On higher integrability of the gradient of solutions to the Zaremba problem for $p$-Laplace equation

Yu. A. Alkhutova, C. D. Apiceb, M. A. Kisatovc, A. G. Chechkinacd

a Vladimir State University, Vladimir, Russian Federation
b University of Salerno, Italia
c Lomonosov Moscow State University, Moscow, Russian Federation
d Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russian Federation
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DOI: https://doi.org/10.31857/S268695432260046X
Abstract: A higher integrability of the gradient of a solution to the Zaremba problem in a bounded Lipschitz plane domain is proved for the inhomogeneous $p$-Laplace equation.
Keywords: Zaremba problem, meyers estimates, $p$-capacity, imbedding theorems, higher integrability.
Funding agency Grant number
Russian Science Foundation 22-21-00292
Program Modeling, Simulation and Optimization Complex Systems
Alkhutov, Kisatov, and Chechkina acknowledge the support of the Russian Science Foundation, project no. 22-21-00292. D’Apice’s research was supported by the program “Modeling, Simulation, and Optimization of Complex Systems”.
Presented: V. V. Kozlov
Received: 13.07.2022
Revised: 22.05.2023
Accepted: 30.05.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue 1, Pages 282–285
DOI: https://doi.org/10.1134/S1064562423700825
Bibliographic databases:
Document Type: Article
UDC: 517.954, 517.982
Language: Russian
Citation: Yu. A. Alkhutov, C. D. Apice, M. A. Kisatov, A. G. Chechkina, “On higher integrability of the gradient of solutions to the Zaremba problem for $p$-Laplace equation”, Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023), 47–51; Dokl. Math., 108:1 (2023), 282–285
Citation in format AMSBIB
\Bibitem{AlkDapKis23}
\by Yu.~A.~Alkhutov, C.~D.~Apice, M.~A.~Kisatov, A.~G.~Chechkina
\paper On higher integrability of the gradient of solutions to the Zaremba problem for $p$-Laplace equation
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 512
\pages 47--51
\mathnet{http://mi.mathnet.ru/danma397}
\crossref{https://doi.org/10.31857/S268695432260046X}
\elib{https://elibrary.ru/item.asp?id=54538843}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue 1
\pages 282--285
\crossref{https://doi.org/10.1134/S1064562423700825}
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