On the symmetry of the boundary conditions of the volume potential

It is well known that the volume potential determines the mass or the charge distributed over the domain with density f. The volume potential is extensively used in function theory and embedding theorems. It is also well known that the volume potential gives a solution to an inhomogeneous equation. And it generates a linear self-adjoint operator. It is known that self-adjoint differential operators are generated by boundary conditions. In our previous papers for an arbitrary domain a boundary condition on the volume potential is given. In the past, it was not possible to prove the self-adjointness of these obtained boundary conditions. In the present paper, we prove the symmetry of boundary condition for the volume potential. © 2017 Author(s).

Авторы
Kal'menov T.S. 1, 2 , Arepova G.1 , Suragan D. 1, 2
Сборник материалов конференции
Язык
Английский
Статус
Опубликовано
Номер
040014
Том
1880
Год
2017
Организации
  • 1 Institute Mathematics and Mathematical Modeling, Almaty, Kazakhstan
  • 2 Nikolskii Institute of Mathematics, Peoples Friendship University of Russia, RUDN University, Moscow, Russian Federation
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5317/