Well-posed problems for the Laplace-Beltrami operator on a punctured two-dimensional sphere
- 23 July 2023
- journal article
- Published by Erdal Karapinar in Advances in the Theory of Nonlinear Analysis and its Application
- Vol. 7 (2), 428-440
- 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
This publication has 12 references indexed in Scilit:
- Correctness of the definition of the Laplace operator with delta-like potentialsComplex Variables and Elliptic Equations, 2020
- The Correct Definition of Second-Order Elliptic Operators with Point Interactions and their ResolventsSiberian Advances in Mathematics, 2020
- Changes in a Finite Part of the Spectrum of the Laplace Operator under Delta-Like PerturbationsDifferential Equations, 2019
- Singular perturbations of Laplace operator and their resolventsComplex Variables and Elliptic Equations, 2019
- Self-adjoint restrictions of maximal operator on graphUfimskii Matematicheskii Zhurnal, 2017
- Resolvents of well-posed problems for finite-rank perturbations of the polyharmonic operator in a punctured domainSiberian Mathematical Journal, 2016
- On Green function's propertiesInternational Journal of Mathematical Analysis, 2013
- Approximation Theory and Harmonic Analysis on Spheres and BallsPublished by Springer Science and Business Media LLC ,2013
- Well-posed problems for the Laplace operator in a punctured diskMathematical Notes, 2011
- The theory of extensions and explicitly-soluble modelsRussian Mathematical Surveys, 1987