Geodesic
The influence of lower derivatives on the solvability of the Dirichlet problem for multidimensional elliptic systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 27-34

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By means of the Fourier transform, we examine the Dirichlet problem for a multidimensional elliptic system containing lower derivatives. We prove that the lower terms significantly influence the solvability of the first boundary value problem for elliptic systems of equations in contrast to the case of a single elliptic equation. The problem is reduced to a single second-order equation; the nature of the solvability of the original problem depends on the type of this equation.
Keywords: elliptic systems, first boundary value problem, Dirichlet problem, lower derivatives
Mots-clés : Fourier transform 
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     title = {The influence of lower derivatives on the solvability of the {Dirichlet} problem for multidimensional elliptic systems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {234},
     year = {2024},
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E. A. Golovko; N. S. Katыapova. The influence of lower derivatives on the solvability of the Dirichlet problem for multidimensional elliptic systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 27-34. http://geodesic.mathdoc.fr/item/INTO_2024_234_a3/