Bull. Korean Math. Soc. 2018; 55(5): 1577-1586
Online first article May 2, 2018 Printed September 30, 2018
https://doi.org/10.4134/BKMS.b170913
Copyright © The Korean Mathematical Society.
Yong Hah Lee
Ewha Womans University
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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