Communications of the
Korean Mathematical Society CKMS

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 $f$.

Keywords: $\mathcal A$-harmonic function, $p$-harmonic boundary, boundary value problem

MSC numbers: 58J05, 31B05