Open AccessON THE SOLVABILITY OF SOME BOUNDARY VALUE PROBLEMS
WITH INVOLUTION
Author(s) -
Kulzina Zh. Nazarova,
Kulzina Zh. Nazarova,
Batirkhan Turmetov,
Б. Х. Турметов,
Kairat I. Usmanov,
Kairat I. Usmanov
Publication year - 2020
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2020-26-3-7-16
Subject(s) - mathematics , boundary value problem , uniqueness , mathematical analysis , trace operator , involution (esoterism) , smoothness , operator (biology) , mixed boundary condition , free boundary problem , elliptic boundary value problem , biochemistry , chemistry , repressor , politics , political science , transcription factor , law , gene
This article is devoted to the study of the solvability of some boundary value problems with involution.In the space Rn, the map Sx=x is introduced. Using this mapping, a nonlocal analogue of the Laplace operator is introduced, as well as a boundary operator with an inclined derivative. Boundary-value problems are studied that generalize the well-known problem with an inclined derivative. Theorems on the existence and uniqueness of the solution of the problems under study are proved. In the Helder class, the smoothness of the solution is also studied. Using well-known statements about solutions of a boundary value problem with an inclined derivative for the classical Poisson equation, exact orders of smoothness of a solution to the problem under study are found.