Well-posed problems for the Laplace-Beltrami operator on a punctured two-dimensional sphere

Year 2023, Volume: 7 Issue: 2, 428 - 440, 23.07.2023

Baltabek Kanguzhin Karlygash Dosmagulova

https://doi.org/10.31197/atnaa.1253855

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 for elliptic equations

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