- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 7 Issue: 2
- Well-posed problems for the Laplace-Beltrami operator on a punctured two-dimensional sphere
Well-posed problems for the Laplace-Beltrami operator on a punctured two-dimensional sphere
Authors : Baltabek Kanguzhin, Karlygash Dosmagulova
Pages : 428-440
Doi:10.31197/atnaa.1253855
View : 34 | Download : 41
Publication Date : 2023-07-23
Article Type : Research Article
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