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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2025, Volume 521, Pages 23–27
DOI: https://doi.org/10.31857/S2686954325010038 (Mi danma615) 		 
MATHEMATICS

Perron's method in the Dirichlet problem for the soft Laplacian on a stratified set

N. S. Dairbekovab, O. M. Penkinbc, D. Savasteevc

a Suleyman Demirel University, Almaty
b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty
c Voronezh State University
DOI: https://doi.org/10.31857/S2686954325010038
Abstract: We prove solvability of the Dirichlet problem for the soft Laplacian on a stratified set basing on a modification of the Perron well-known method.
Keywords: stratified measure, soft Laplacian, mean value theorem, Harnack's inequality, Harnack convergence theorem.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan BR20281002
This work was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan, project BR20281002.
Presented: I. A. Taimanov
Received: 12.12.2024
Revised: 20.01.2025
Accepted: 20.01.2025
English version:
Doklady Mathematics, 2025, Volume 111, Issue 1, Pages 16–19
DOI: https://doi.org/10.1134/S1064562424602658
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: N. S. Dairbekov, O. M. Penkin, D. Savasteev, “Perron's method in the Dirichlet problem for the soft Laplacian on a stratified set”, Dokl. RAN. Math. Inf. Proc. Upr., 521 (2025), 23–27; Dokl. Math., 111:1 (2025), 16–19
Citation in format AMSBIB
\Bibitem{DaiPenSav25}
\by N.~S.~Dairbekov, O.~M.~Penkin, D.~Savasteev
\paper Perron's method in the Dirichlet problem for the soft Laplacian on a stratified set
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2025
\vol 521
\pages 23--27
\mathnet{http://mi.mathnet.ru/danma615}
\elib{https://elibrary.ru/item.asp?id=80559502}
\transl
\jour Dokl. Math.
\yr 2025
\vol 111
\issue 1
\pages 16--19
\crossref{https://doi.org/10.1134/S1064562424602658}
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