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.
Bibliographical noteFunding 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).
© 2017 Korean Mathematical Society.
- A-harmonic function
- Boundary value problem
- P-harmonic boundary