Uniqueness set for the single-layer potential

Authors

  • Svidlov A.A. Kuban State University, Krasnodar, Российская Федерация
  • Drobotenko M.I. Kuban State University, Krasnodar, Российская Федерация
  • Biryuk A.E. Kuban State University, Krasnodar, Российская Федерация

UDC

519.63

Abstract

The work is devoted to the question of completeness of the system of point potentials. We introduce the concept of a uniqueness set for the single-layer potential and prove that the system of point potential is complete if and only if the set of basis points (singularities) of potentials is a uniqueness set for the single-layer potential. We study properties of the introduced uniqueness sets (for the single layer potential) and give examples of sets that are uniqueness sets and those are not. We show that the new concept extends the concept of uniqueness set of harmonic functions. We give an example of a set of points, which is not a set of uniqueness of harmonic functions, however the corresponding system of point potential is complete. This set is a uniqueness set for the single-layer potential.

Keywords:

fundamental solutions method, point potentials method, basis potentials method

Author Infos

Aleksandr A. Svidlov

канд. физ.-мат. наук, старший преподаватель кафедры теории функций Кубанского государственного университета

e-mail: svidlov@mail.ru

Mikhail I. Drobotenko

канд. физ.-мат. наук, доцент кафедры математических и компьютерных методов Кубанского государственного университета

e-mail: mdrobotenko@mail.ru

Andrey E. Biryuk

канд. физ.-мат. наук, доцент кафедры теории функций Кубанского государственного университета

e-mail: abiryuk@gmail.ru

References

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Issue

2015. No. 2

Pages

77-81

Submitted

2015-04-03

Published

2015-06-25

How to Cite

Svidlov A.A., Drobotenko M.I., Biryuk A.E. Uniqueness set for the single-layer potential. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2015, no. 2, pp. 77-81. (In Russian)

Copyright (c) 2015 Svidlov A.A., Drobotenko M.I., Biryuk A.E.

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This work is licensed under a Creative Commons Attribution 4.0 International License.