Presentation of the sum of regular elliptic operator and degenerate elliptic operators of higher order as a composition

Author(s):  A.V. Glushak , Dr., Prof., Belgorod National Research University, Belgorod, Russia, Glushak@.bsu.edu.ru

Issue:  Volume 50, № 2

Rubric:  Mathematics

Annotation:  The partial differential equation considered in this paper refers to a class of equations with a nonnegative characteristic form, also called degenerate elliptic equations. Some problems of hydromechanics, gas dynamics, filtration theory, etc. lead to the study of such problems. The main attention is paid to the investigation of the solvability of boundary problems. In this paper we establish a representation of the sum of a regular elliptic operator and degenerate elliptic operators in the form of a composition of operators similar in structure, which will allow us to further investigate the unique solvability of the corresponding boundary value problem.

Keywords:  degenerate high-order elliptic differential operators, composition.

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