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

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

Kaynakça

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