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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 218, Number 1, Pages 3–22
DOI: https://doi.org/10.4213/tmf10522 (Mi tmf10522) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky–Meyers estimate

Yu. A. Alkhutova, G. A. Chechkinbcd

a Vladimir State University named after Alexander and Nikolay Stoletov, Vladimir, Russia
b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty, Kazakhstaт
c Lomonosov Moscow State University, Moscow, Russia
d Institute of Mathematics with Computing Center, Ufa Federal Research Centre, Russian Academy of Sciences, Ufa, Russia
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DOI: https://doi.org/10.4213/tmf10522
Abstract: We prove the higher integrability of the gradient of solutions of the Zaremba problem in a bounded strongly Lipschitz domain for an inhomogeneous $p(\,\cdot\,)$-Laplace equation with a variable exponent $p$ having a logarithmic continuity modulus.
Keywords: Zaremba problem, Meyers estimates, capacity, embedding theorems, higher integrability.
Funding agency Grant number
Russian Science Foundation 22-21-00292
20-11-20272
Ministry of Science and Higher Education of the Russian Federation FZUN-2023-0004
Ministry of Education and Science of the Republic of Kazakhstan АР14869553
The results in Sec. 3 belong to the first author. The proof of Lemma 1 and Theorem 1 of that section was supported by a grant from the Russian Science Foundation (project No. 22-21-00292), and the proof of Theorem 2 was supported by the State Assignment of the Vladimir State University (FZUN-2023-0004). The results of the second author in Sec. 2 were supported by a grant of the Russian Science Foundation (project No. 20-11-20272); and those in Sec. 1, by the grant from the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan (project AP14869553).
Received: 24.04.2023
Revised: 12.05.2023
English version:
Theoretical and Mathematical Physics, 2024, Volume 218, Issue 1, Pages 1–18
DOI: https://doi.org/10.1134/S004057792401001X
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Document Type: Article
Language: Russian
Citation: Yu. A. Alkhutov, G. A. Chechkin, “Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky–Meyers estimate”, TMF, 218:1 (2024), 3–22; Theoret. and Math. Phys., 218:1 (2024), 1–18
Citation in format AMSBIB
\Bibitem{AlkChe24}
\by Yu.~A.~Alkhutov, G.~A.~Chechkin
\paper Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky--Meyers estimate
\jour TMF
\yr 2024
\vol 218
\issue 1
\pages 3--22
\mathnet{http://mi.mathnet.ru/tmf10522}
\crossref{https://doi.org/10.4213/tmf10522}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4700040}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...218....1A}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 218
\issue 1
\pages 1--18
\crossref{https://doi.org/10.1134/S004057792401001X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85183758193}
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    • This publication is cited in the following 1 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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