Nonlocal vector calculus on the sphere
Abstract
We introduce a nonlocal vector calculus on the unit two-sphere using weakly singular integral operators. Within this framework, the operators are diagonalizable in terms of scalar and vector spherical harmonics, a property that facilitates the proof of a nonlocal Stokes theorem. This constitutes the first instance of such a theorem on a curved surface. Furthermore, our analysis demonstrates the strong convergence of these nonlocal operators to the classical differential operators of vector calculus as the interaction range tends to zero.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Differential Equations and Boundary Problems
Matrix Theory and Algorithms
Publication details
- Journal / source
- Mathematical Models and Methods in Applied Sciences
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 36
- Issue
- 10
- Pages
- 2163–2195
- Publication date
- 29 April 2026
- Language
- EN