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http://dx.doi.org/10.4134/BKMS.b170913

UNIQUENESS OF SOLUTIONS OF A CERTAIN NONLINEAR ELLIPTIC EQUATION ON RIEMANNIAN MANIFOLDS  

Lee, Yong Hah (Department of Mathematics Education Ewha Womans University)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.5, 2018 , pp. 1577-1586 More about this Journal
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;
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