Uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators via $p$-harmonic boundary
Commun. Korean Math. Soc. 2017 Vol. 32, No. 4, 1025-1031
https://doi.org/10.4134/CKMS.c160233
Published online October 31, 2017
Yong Hah Lee
Ewha Womans University
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 $f$.
Keywords : $\mathcal A$-harmonic function, $p$-harmonic boundary, boundary value problem
MSC numbers : 58J05, 31B05
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