Asymptotic behavior of $\mathcal A$-harmonic functions and $p$-extremal length
Bull. Korean Math. Soc. 2010 Vol. 47, No. 2, 423-432
https://doi.org/10.4134/BKMS.2010.47.2.423
Printed March 1, 2010
Seok Woo Kim, Sang Moon Lee, and Yong Hah Lee
Konkuk University, Konkuk University, and Ewha Womans University
Abstract : We describe the asymptotic behavior of functions of the Royden $p$-algebra in terms of $p$-extremal length. We also prove that each bounded $\mathcal A$-harmonic function with finite energy on a complete Riemannian manifold is uniquely determined by the behavior of the function along $p$-almost every curve.
Keywords : $\mathcal A$-harmonic function, $p$-harmonic boundary, comparison principle, maximum principle, $p$-extremal length, $p$-almost every curve
MSC numbers : 58J05, 31B05
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