Bull. Korean Math. Soc. 2010; 47(2): 423-432
Printed March 1, 2010
https://doi.org/10.4134/BKMS.2010.47.2.423
Copyright © The Korean Mathematical Society.
Seok Woo Kim, Sang Moon Lee, and Yong Hah Lee
Konkuk University, Konkuk University, and Ewha Womans University
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
2012; 49(6): 1241-1250
2023; 60(2): 495-505
2019; 56(5): 1211-1217
2014; 51(6): 1591-1603
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd