On the symmetry of the boundary conditions of the volume potential

Tynysbek Sh. Kalmenov, Gaukhar D. Arepova, Durvudkhan Suragan

2017

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DOI 10.1063/1.5000630
Data confidence 70 medium
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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.