Well-Posed Problems for the Laplace–Beltrami Operator on a Punctured Two-Dimensional Sphere

Open Access

Original research article

Author(s):

Baltabek Kanguzhin^a, Karlygash Dosmagulova^b

^a Department of Mathematics, Al-Farabi Kazakh National University, Almaty, Kazakhstan.
^b Department of Mathematics, Al-Farabi Kazakh National University, Almaty, Kazakhstan; Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium.

Advances in the Theory of Nonlinear Analysis and its Applications 7(2), 428-440.

Received: August 1, 2022

Accepted: May 28, 2023

Published: June 14, 2023

Abstract

An arbitrary point is removed from a three-dimensional Euclidean space on a two-dimensional sphere. The new well-posed solvable boundary value problems for the corresponding Laplace–Beltrami operator on the resulting punctured sphere are presented. To formulate the well-posed problems, some properties of Green’s function of the Laplace–Beltrami operator on a two-dimensional sphere are previously studied in detail.

Keywords: Laplace–Beltrami operator, two-dimensional punctured sphere, well-posed problems, Green’s functions, elliptic equations.

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APA Style

Kanguzhin, B., & Dosmagulova, K. (2023). Well-posed problems for the Laplace-Beltrami operator on a punctured two-dimensional sphere. Advances in the Theory of Nonlinear Analysis and its Application, 7(2), 428-440.