Geodesic
Nonlocal boundary value problems for a three-dimensional elliptic equation with singular coefficients in a semi-infinite parallelepiped
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 161-178

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The investigated two nonlocal problems for an elliptic equation with two singular coefficients in a semi-infinite parallelepiped. The proof of the uniqueness of the solution and its construction is carried out by the method of spectral analysis. The solution to the problem is constructed as the sum of the biorthogonal series. In substantiating the uniform convergence of the constructed series, we used asymptotic estimates of the Bessel functions of the real and imaginary argument. Based on them, estimates are obtained for each member of the series, which made it possible to prove the convergence of the resulting series and its derivatives to the second order inclusive, as well as the existence theorem in the class of regular solutions.
Mots-clés : equations of elliptic type, singular coefficient, biorthogonal series
Keywords: nonlocal problem, spectral method, semi-infinite parallelepiped. 
@article{SEMR_2020_17_a81,
     author = {A. K. Urinov and K. T. Karimov},
     title = {Nonlocal boundary value problems for a three-dimensional elliptic equation with singular coefficients in a semi-infinite parallelepiped},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {161--178},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a81/}
}
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A. K. Urinov; K. T. Karimov. Nonlocal boundary value problems for a three-dimensional elliptic equation with singular coefficients in a semi-infinite parallelepiped. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 161-178. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a81/