Uniquely solvable problems for the Laplace-Beltrami operator on a sphere punctured by a curve

Uniquely solvable problems for the Laplace-Beltrami operator


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Authors

  • Karlygash Dosmagulova Al-Farabi Kazakh National University
  • Baltabek Kanguzhin Al-Farabi Kazakh National University

Keywords:

Laplace-Beltrami operator, single and double layer potentials, two-dimensional sphere

Abstract

A fixed smooth arc is removed from a two-dimensional sphere of three-dimensional space. The Laplace-Beltrami operator is studied on the resulting surface. In the paper the boundary conditions on a remote arc are found, which guarantee the existence of a unique solution to the inhomogeneous Laplace-Beltrami equation.

Author Biography

Baltabek Kanguzhin, Al-Farabi Kazakh National University

Professor of Mathematics

References

bibitem{JL} John M.Lee, Riemannian manifolds, Graduate text in Mathematics. Springer ISBN 0-387-98271-X.

bibitem{GNS} S. Gemmrich, N. Nigam 1, O. Steinbach, Boundary Integral Equations for the Laplace–Beltrami Operator, https://arxiv.org/abs/1111.6962v1.

bibitem{Zo} V.A. Zorich, Mathematical analysis II, Springer (2004) ISBN 3-540-40633-6.

bibitem{KS} T.Sh. Kal'menov, D. Suragan, On permeable potential boundary conditions for the Laplace–Beltrami operator, Sib. Math. J. 56(6) (2015) 1060-1064 https://doi.org/10.1134/S0037446615060099.

bibitem{KD} B.E. Kanguzhin, K.A. Dosmagulova, Well-posed problems for the Laplace-Beltrami operator on a punctured two-dimensional sphere, Adv. Theory Nonlinear Anal. Appl. 7(2) (2023) 1253855, https://doi.org/10.31197/atnaa.1253855.

bibitem{DKF} K. Dosmagulova, B. Kanguzhin, Z. Fazullin, Spectrum of a Perturbed Harmonic Oscillator, Appl. Math. Inf. Sci. 17(4) (2023) 553-557 https://doi.org/10.18576/amis/170403.

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Published

2023-09-17

How to Cite

Dosmagulova, K., & Kanguzhin, B. (2023). Uniquely solvable problems for the Laplace-Beltrami operator on a sphere punctured by a curve: Uniquely solvable problems for the Laplace-Beltrami operator. Results in Nonlinear Analysis, 6(3), 43–49. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/260

Issue

Vol. 6 No. 3 (2023): volume 6 issue 3

Section

Articles

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Copyright (c) 2023 Results in Nonlinear Analysis

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