G. Z. Khabibullina, S. V. Makletsov, R. M. Mavlyaviev, “Integral representation of a solution to three-dimensional elliptic equation with strong degeneration”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 11,Pages <nobr>73

Integral representation of a solution to three-dimensional elliptic equation with strong degeneration

G. Z. Khabibullina^a, S. V. Makletsov^b, R. M. Mavlyaviev^c

^a Chair of Theory and Principles of Physics and Information Science Teaching, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
^b Chair of Function Theory and Approximations, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
^c Chair of Higher Mathematics and Mathematical Modeling, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: In a three-dimentional Euclidean space we consider an elliptic equation with strong degeneration. We derive the first and the second Green formula. We also construct a fundamental solution to the equation and obtain an integral representation of its solution.

Keywords: degenerate elliptic equations, fundamental solution, integral representation of the solution.

UDC: 517.95

Received: 17.04.2014