Uniqueness of solutions of a certain nonlinear elliptic equation on Riemannian manifolds

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 $p$-nonparab...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2018, 55(5), , pp.1577-1586
Main Author: 이용하
Format: Article
Language:English
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수학
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Summary: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. KCI Citation Count: 0
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.b170913