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Contemporary Mathematics. Fundamental Directions, 2024, Volume 70, Issue 1, Pages 1–14
DOI: https://doi.org/10.22363/2413-3639-2024-70-1-1-14 (Mi cmfd525) 		 
On the Boyarsky–Meyers estimate for the solution of the Dirichlet problem for a second-order linear elliptic equation with drift

Yu. A. Alkhutova, G. A. Chechkinbcd

a Vladimir State University named after Alexander and Nikolay Stoletovs, Vladimir, Russia
b Lomonosov Moscow State University, Moscow, Russia
c Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
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/10.22363/2413-3639-2024-70-1-1-14
Abstract: We establish the increased integrability of the gradient of the solution to the Dirichlet problem for the Laplace operator with lower terms and prove the unique solvability of this problem.
Keywords: Zaremba problem, Meyers estimates, embedding theorems, increased integrability.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FZUN-2023-0004
Russian Science Foundation 20-11-20272
Ministry of Education and Science of the Republic of Kazakhstan AP14869553
The results of the first author in section 3 were obtained within the framework of the state assignment of the Vladimir State University (project FZUN-2023-0004), and the results of the second author in section 2 were supported by the grant of the Russian Science Foundation (project 20-11-20272). The results of the second author in section 1 were partially supported by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (grant AP14869553).
Bibliographic databases:
Document Type: Article
UDC: 517.954
Language: Russian
Citation: Yu. A. Alkhutov, G. A. Chechkin, “On the Boyarsky–Meyers estimate for the solution of the Dirichlet problem for a second-order linear elliptic equation with drift”, Functional spaces. Differential operators. Problems of mathematics education, CMFD, 70, no. 1, PFUR, M., 2024, 1–14
Citation in format AMSBIB
\Bibitem{AlkChe24}
\by Yu.~A.~Alkhutov, G.~A.~Chechkin
\paper On the Boyarsky--Meyers estimate for the solution of the Dirichlet problem for a second-order linear elliptic equation with drift
\inbook Functional spaces. Differential operators. Problems of mathematics education
\serial CMFD
\yr 2024
\vol 70
\issue 1
\pages 1--14
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd525}
\crossref{https://doi.org/10.22363/2413-3639-2024-70-1-1-14}
\edn{https://elibrary.ru/ZXGOMR}
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