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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 7, Pages 58–72
DOI: https://doi.org/10.26907/0021-3446-2022-7-58-72 (Mi ivm9793) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain

T. G. Ergasheva, Z. R. Tulakovab

a «Tashkent Institute of Irrigation and Agricultural Mechanization Engineers» National Research University, 39 Kari Niyazi str., Tashkent, 100000 Republic of Uzbekistan
b Fergana Branch of the Tashkent University of Information Technologies, 185 Mustakillik str., Fergana, 100118 Republic of Uzbekistan
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DOI: https://doi.org/10.26907/0021-3446-2022-7-58-72
Abstract: 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.
Received: 28.09.2021
Revised: 11.11.2021
Accepted: 23.12.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 7, Pages 51–63
DOI: https://doi.org/10.3103/S1066369X22070039
Document Type: Article
UDC: 517.946
Language: Russian
Citation: T. G. Ergashev, Z. R. Tulakova, “A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 7, 58–72; Russian Math. (Iz. VUZ), 66:7 (2022), 51–63
Citation in format AMSBIB
\Bibitem{ErgTul22}
\by T.~G.~Ergashev, Z.~R.~Tulakova
\paper A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 7
\pages 58--72
\mathnet{http://mi.mathnet.ru/ivm9793}
\crossref{https://doi.org/10.26907/0021-3446-2022-7-58-72}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 7
\pages 51--63
\crossref{https://doi.org/10.3103/S1066369X22070039}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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