A. S. Berdyshev, A. Hasanov, A. Ryskan, “A boundary-value problem for a class of four-dimensional degenerate elliptic equations”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2021, Volume 194,Pages <nobr>55

A boundary-value problem for a class of four-dimensional degenerate elliptic equations

A. S. Berdyshev^ab, A. Hasanov^c, A. Ryskan^ab

^a Kazakh National Pedagogical University
^b Institute of Information and Computational Technologies, Ministry of Education and Science, Republic of Kazakhstan
^c V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan

Abstract: The solvability of the problem with mixed Neumann–Dirichlet conditions for a degenerate four-dimensional elliptic equation are studied. The uniqueness of a solution to the problem is proved by the method based on the energy integral.

Keywords: degenerate four-dimensional elliptic equation, boundary-value problem with Neumann–Dirichlet conditions, Gellerstedt equation in four variables, fundamental solution, Lauricella and Gauss hypergeometric functions.

UDC: 517.956

MSC: 35J25, 35J70

DOI: 10.36535/0233-6723-2021-194-55-70