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Symposium Functional Analysis in Interdisciplinary Applications

FAIA 2017: Functional Analysis in Interdisciplinary Applications pp 272–288Cite as

Internal Boundary Value Problems for the Laplace Operator with Singularity Propagation

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 216))

Abstract

We consider well-posedness issues of problems of the Laplace operator in the unit circle with two internal points. For boundary value problems, one of the main issues is the well-posedness of the problem. When the problem is considered in a non-simply-connected domain, there usually appear additional conditions depending on the features of the domain under consideration. If for the well-posedness of the problem, in addition to the boundary conditions, one requires to take into account the internal communications of the domain, then such problems are called internal boundary value problems. For such problems there is written out a class of functions in which there exist such kinds of well-posed problems. A constructive method for constructing solutions to such problems is developed. As an illustration, examples are considered.

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Acknowledgements

Research supported by the target program 0085/PTSF-14 of the Ministry of Education and Science of Republic of Kazakhstan.

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Authors and Affiliations

  1. S. Seifullin Kazakh agrotechnical university, 62 Zhenis avenue, Astana, 010011, Kazakhstan

    Daulet B. Nurakhmetov & Almir A. Aniyarov

Authors
  1. Daulet B. Nurakhmetov
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  2. Almir A. Aniyarov
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Corresponding author

Correspondence to Daulet B. Nurakhmetov .

Editor information

Editors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Tynysbek Sh. Kalmenov

  2. Department of Mechanics and Mathematics, Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan

    Erlan D. Nursultanov

  3. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

  4. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Makhmud A. Sadybekov

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Nurakhmetov, D.B., Aniyarov, A.A. (2017). Internal Boundary Value Problems for the Laplace Operator with Singularity Propagation. In: Kalmenov, T., Nursultanov, E., Ruzhansky, M., Sadybekov, M. (eds) Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-67053-9_26

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