About the index for one boundary value problem

Authors

  • Victor Polunin Belgorod State Technological University named after V. G. Shukhov
  • Lidiya Kovaleva Belgorod State National Research University

DOI:

https://doi.org/10.52575/2687-0959-2023-55-1-29-38

Keywords:

Dirichlet Problem, Two-Dimensional Complex, Riemann Problem, Index of the Problem, Helder Space with Weight

Abstract

In the 3D space, a boundary value problem for an elliptic equation on a two-dimensional complex is considered. The Dirichlet condition is set on the boundary of a two-dimensional complex. Within the framework of the functional-theoretic approach, this problem is reduced to a non-local Riemann boundary value problem. The solution of the problem is sought in Helder spaces with weight. The Fredholm solvability of the Dirichlet problem on a two-dimensional complex is proved in the article. The index for the formulated problem is calculated.

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Author Biographies

Victor Polunin, Belgorod State Technological University named after V. G. Shukhov

PhD, Associate Professor, Associate Professor of the Department of of Higher Mathematics, Institute of Economics and Management

Lidiya Kovaleva, Belgorod State National Research University

PhD, Associate Professor of the Department of Applied Mathematics and Computer Modeling of the Institute of Engineering and Digital Technologies

References

Ковалева Л. А., Солдатов А. П. 2007. Об одной задаче теории функций. Доклады Адыгской (Черкесской) международной академии наук, 9(2): 30–38.

Ковалева Л. А., Солдатов А. П. 2015. Задача Дирихле на двумерных стратифицированных множествах. Изв. РАН, сер. Матем., 79(1): 77–114.

Овчинников Ю. Н., Лукьянчук И. А. 2002. Проводимость и распределение токов в двухкомпонентной системе состоящей из правильных треугольников. ЖЭТФ, 121(1): 239–252.

Покорный Ю. В. 2004. Дифференциальные уравнения на геометрических графах. М.: Физматлит, 272с.

Солдатов А. П. 2005. Элементы функционального анализа и теории функций. Изд-во БелГУ, 140 с.

Солдатов А. П. 1992. Метод теоpии функций в эллиптических кpаевых задачах на плоскости. II. Кусочно-гладкий случай. Изв. АH СССР, 56(3): 566–604.

Солдатов А. П. 1998. Обобщенная задача Римана на римановой поверхности. Докл. РАH, 362(6): 735–738.

Lumer G. 1980. Espases ramifes et diffusion sur les reseaux topologiques. C. R. Acad. Sc. Paris. Serie A. 291: 219–234.

Penkin O. M. 2004. Second-order elliptic equations on a stratified set. Differential equations on networks. J. Math. Sci. (N. Y.). 119(6): 836–867.


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Published

2023-03-30

How to Cite

Polunin, V., & Kovaleva, L. (2023). About the index for one boundary value problem. Applied Mathematics & Physics, 55(1), 29-38. https://doi.org/10.52575/2687-0959-2023-55-1-29-38

Issue

Vol. 55 No. 1 (2023)

Section

Mathematics

Copyright (c) 2023 Applied Mathematics & Physics

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