Geodesic
A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2022), pp. 58-72

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Solutions of the Dirichlet and Neumann problems for multidimensional singular elliptic equations in an infinite domain were found in explicit forms in recent works of the authors. In this paper, a problem with mixed conditions, which is a natural generalization of the previously considered Dirichlet and Neumann problems, is studied. In proving the existence of a unique solution to the problem posed, representation of the multiple Lauricella hypergeometric function at limiting values of the variables and a new formula for multiple improper integrals, which generalizes the well-known formula from the handbook of I.S. Gradshtein and I.M. Ryzhik, are used.
Keywords: Problem with mixed boundary conditions in an infinite domain, multidimensional elliptic equation with singular coefficients, fundamental solution, formula for the limit values of a hypergeometric function, Lauricella hypergeometric function of several variables. 
@article{IVM_2022_7_a5,
     author = {T. G. Ergashev and Z. R. Tulakova},
     title = {A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {58--72},
     publisher = {mathdoc},
     number = {7},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_7_a5/}
}
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T. G. Ergashev; Z. R. Tulakova. A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2022), pp. 58-72. http://geodesic.mathdoc.fr/item/IVM_2022_7_a5/