On the symmetry of the boundary conditions of the volume potential

Tynysbek Sh Kal'menov; Gaukhar Arepova; Durvudkhan Suragan

doi:10.1063/1.5000630

On the symmetry of the boundary conditions of the volume potential

Tynysbek Sh Kal'menov, Gaukhar Arepova, Durvudkhan Suragan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

Abstract

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.

Original language	English
Title of host publication	International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017
Editors	Tynysbek Kal'menov, Makhmud Sadybekov
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735415607
DOIs	https://doi.org/10.1063/1.5000630
Publication status	Published - Sept 11 2017
Externally published	Yes
Event	International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017 - Astana, Kazakhstan Duration: Oct 2 2017 → Oct 5 2017

Publication series

Name	AIP Conference Proceedings
Volume	1880
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017
Country/Territory	Kazakhstan
City	Astana
Period	10/2/17 → 10/5/17

ASJC Scopus subject areas

General Physics and Astronomy

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10.1063/1.5000630

Cite this

Kal'menov, T. S., Arepova, G., & Suragan, D. (2017). On the symmetry of the boundary conditions of the volume potential. In T. Kal'menov, & M. Sadybekov (Eds.), International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017 Article 040014 (AIP Conference Proceedings; Vol. 1880). American Institute of Physics Inc.. https://doi.org/10.1063/1.5000630

On the symmetry of the boundary conditions of the volume potential. / Kal'menov, Tynysbek Sh; Arepova, Gaukhar; Suragan, Durvudkhan.
International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017. ed. / Tynysbek Kal'menov; Makhmud Sadybekov. American Institute of Physics Inc., 2017. 040014 (AIP Conference Proceedings; Vol. 1880).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kal'menov, TS, Arepova, G & Suragan, D 2017, On the symmetry of the boundary conditions of the volume potential. in T Kal'menov & M Sadybekov (eds), International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017., 040014, AIP Conference Proceedings, vol. 1880, American Institute of Physics Inc., International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017, Astana, Kazakhstan, 10/2/17. https://doi.org/10.1063/1.5000630

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N2 - 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.

AB - 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.

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On the symmetry of the boundary conditions of the volume potential

Abstract

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