Uniqueness of solutions of a certain nonlinear elliptic equation on Riemannian manifolds
Bull. Korean Math. Soc. 2018 Vol. 55, No. 5, 1577-1586
Published online September 30, 2018
Yong Hah Lee
Ewha Womans University
Abstract : In this paper, we prove that if every bounded $\mathcal A$-harmonic function on a complete Riemannian manifold $M$ is asymptotically constant at infinity of $p$-nonparabolic ends of $M$, then each bounded $\mathcal A$-harmonic function is uniquely determined by the values at infinity of $p$-nonparabolic ends of $M$, where $\mathcal A$ is a nonlinear elliptic operator of type $p$ on $M$. Furthermore, in this case, every bounded $\mathcal A$-harmonic function on $M$ has finite energy.
Keywords : $\mathcal A$-harmonic function, end, $p$-parabolicity, uniqueness
MSC numbers : 58J05, 31B05
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