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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 212, Pages 43–49
DOI: https://doi.org/10.36535/0233-6723-2022-212-43-49 (Mi into1032) 		 
On strongly coupled multidimensional elliptic systems

E. A. Golovko

Irkutsk State University
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DOI: https://doi.org/10.36535/0233-6723-2022-212-43-49
Abstract: The article investigates the Dirichlet problem in a half-space for an elliptic system as per Petrovsky of three equations with three unknown functions depending on three independent variables. Conditions for violation of the Noetherian property of the problem in a concrete half-space are found. It is shown that the strong connectedness of the system does not imply the violation of the Noetherian property of the Dirichlet problem in any half-space.
Keywords: multidimensional elliptic system, strongly coupled systems, Dirichlet problem, multidimensional analog of the Bitsadze system, violation of the Noether property.
Document Type: Article
UDC: 517.956.2
MSC: 35J57
Language: Russian
Citation: E. A. Golovko, “On strongly coupled multidimensional elliptic systems”, Geometry, Mechanics, and Differential Equations, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 212, VINITI, Moscow, 2022, 43–49
Citation in format AMSBIB
\Bibitem{Gol22}
\by E.~A.~Golovko
\paper On strongly coupled multidimensional elliptic systems
\inbook Geometry, Mechanics, and Differential Equations
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 212
\pages 43--49
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1032}
\crossref{https://doi.org/10.36535/0233-6723-2022-212-43-49}
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