Abstract
We prove the uniqueness of solutions for the boundary value problem of harmonic maps in the setting: given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a regular geodesic ball, there exists a unique harmonic map, which is a limit of a sequence of harmonic maps with finite total energy in the sense of the supremum norm, from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.
| Original language | English |
|---|---|
| Pages (from-to) | 2733-2743 |
| Number of pages | 11 |
| Journal | Bulletin of the Malaysian Mathematical Sciences Society |
| Volume | 43 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 May 2020 |
Bibliographical note
Publisher Copyright:© 2019, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.
Keywords
- Boundary value problem
- Harmonic boundary
- Harmonic map
- Uniqueness