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ЖУРНАЛЫ // Eurasian Mathematical Journal // Архив

Eurasian Math. J., 2020, том 11, номер 2, страницы 93–97 (Mi emj369)

Эта публикация цитируется в 5 статьях

Short communications

Solution of the Neumann problem for one four-dimensional elliptic equation

A. S. Berdysheva, A. Hasanovb, A. R. Ryskana

a Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, 86 Tole bi St, 050012 Almaty, Kazakhstan
b Institute of Mathematics, Uzbek Academy of Sciences, 29 Durmon yuli St, 100125 Tashkent, Uzbekistan

Аннотация: In this article we investigate the Neumann problem for a degenerate elliptic equation in four variables. A fundamental solution is used to construct a solution to the problem. The fundamental solutions are written by using the Lauricella's hypergeometric functions. The energyintegral method is used to prove the uniqueness of the solution to the problem under consideration. In the course of proving the existence of the problem solution, differentiation formulas, decomposition formulas, some adjacent relations formulas and the autotransformation formula of hypergeometric functions are used. The Gauss–Ostrogradsky formula is used to express problem's solution in an explicit form.

Ключевые слова и фразы: Neumann problem, energy-integral method, degenerate four-dimensional elliptic equation, Gauss–Ostrogradsky formula, fundamental solutions, Lauricella hypergeometric functions.

MSC: 35J25, 35J70

Поступила в редакцию: 15.09.2019

Язык публикации: английский

DOI: 10.32523/2077-9879-2020-11-2-93-97



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