Geodesic
Dirichlet problem in parallelepiped for elliptic equation with three singular coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 3-14

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For analog Helmholz biaxisymmetric equation for the case of three variable, we consider Dirichlet problem in parallelepiped. We prove uniqueness of Dirichlet problem solution using spectral analysis methods. We construct the Dirichlet problem solution as double series. In constructing the solutions we use Fourier–Bessel series. We find boundary function the conditions, then the corresponding series converges uniformly.
Keywords: equation with singular coefficients, Dirichlet problem, spectral method, Bessel functions, double row. 
@article{IVM_2019_10_a0,
     author = {A. A. Abashkin and I. P. Egorova},
     title = {Dirichlet problem in parallelepiped for elliptic equation with three singular coefficients},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--14},
     publisher = {mathdoc},
     number = {10},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_10_a0/}
}
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A. A. Abashkin; I. P. Egorova. Dirichlet problem in parallelepiped for elliptic equation with three singular coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 3-14. http://geodesic.mathdoc.fr/item/IVM_2019_10_a0/