Abstract
We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.
| Original language | English |
|---|---|
| Pages (from-to) | 1025-1031 |
| Number of pages | 7 |
| Journal | Communications of the Korean Mathematical Society |
| Volume | 32 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2017 |
Bibliographical note
Funding Information:Received November 7, 2016; Accepted February 2, 2017. 2010 Mathematics Subject Classification. 58J05, 31B05. Key words and phrases. A-harmonic function, p-harmonic boundary, boundary value problem. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2012006926).
Publisher Copyright:
© 2017 Korean Mathematical Society.
Keywords
- A-harmonic function
- Boundary value problem
- P-harmonic boundary