Geodesic
On strongly coupled multidimensional elliptic systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 212 (2022), pp. 43-49

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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. 
@article{INTO_2022_212_a3,
     author = {E. A. Golovko},
     title = {On strongly coupled multidimensional elliptic systems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {43--49},
     publisher = {mathdoc},
     volume = {212},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_212_a3/}
}
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E. A. Golovko. On strongly coupled multidimensional elliptic systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 212 (2022), pp. 43-49. http://geodesic.mathdoc.fr/item/INTO_2022_212_a3/