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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 10, Pages 70–76
DOI: https://doi.org/10.26907/0021-3446-2023-10-70-76 (Mi ivm9942) 		 
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Integral estimates of solutions to boundary values problems for the Poisson equation

F. G. Avkhadieva, A. R. Kacimovb

a Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
b Sultan Qaboos University, Al-Khod 123, PO Box 34, Sultanate Oman
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DOI: https://doi.org/10.26907/0021-3446-2023-10-70-76
Abstract: We consider solutions to two boundary values problems for the Poisson equation on plane domains. We prove several estimates for integrals of solutions using geometric characteristics of domains.
Keywords: Poisson equation, Dirichlet problem, boundary values problem, isoperimetric inequality.
Funding agency Grant number
Russian Science Foundation 23-11-00066
Sultan Qaboos University IG/VC/WRC/21/01
IG/AGR/SWAE/22/02
DR/RG/17
Received: 10.07.2023
Revised: 19.07.2023
Accepted: 26.09.2023
Document Type: Article
UDC: 517.95
Language: Russian
Citation: F. G. Avkhadiev, A. R. Kacimov, “Integral estimates of solutions to boundary values problems for the Poisson equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 10, 70–76
Citation in format AMSBIB
\Bibitem{AvkKac23}
\by F.~G.~Avkhadiev, A.~R.~Kacimov
\paper Integral estimates of solutions to boundary values problems for the Poisson equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 10
\pages 70--76
\mathnet{http://mi.mathnet.ru/ivm9942}
\crossref{https://doi.org/10.26907/0021-3446-2023-10-70-76}
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