Geodesic
Nonlocal problem for a three-dimensional elliptic equation with singular coefficients in a rectangular parallelepiped
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 533-546

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The nonlocal problem for an elliptic equation with two singular coefficients in a rectangular parallelepiped is studied. The uniqueness of the solution of the problem is proved with the use of the method of energy integrals. The spectral Fourier method based on the separation of variables is used to prove the existence of solutions. The solution of the problem is constructed as double Fourier series in terms of a sum of trigonometric and Bessel functions. Under some conditions on parameters and given functions the uniform convergence of the constructed series and its derivatives up to the second order inclusive is proved.
Keywords: nonlocal problem, spectral method, parallelepiped.
Mots-clés : elliptic type equation, singular coefficient 
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     author = {Kamoliddin T. Karimov},
     title = {Nonlocal problem for a three-dimensional elliptic equation with singular coefficients in a rectangular parallelepiped},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a1/}
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Kamoliddin T. Karimov. Nonlocal problem for a three-dimensional elliptic equation with singular coefficients in a rectangular parallelepiped. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 533-546. http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a1/