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Bull. Korean Math. Soc. 2012; 49(6): 1241-1250
Printed November 30, 2012
https://doi.org/10.4134/BKMS.2012.49.6.1241
Copyright © The Korean Mathematical Society.
Maximum principle and comparison principle of $p$-harmonic functions via $p$-harmonic boundary of graphs
Yong Hah Lee
Ewha Womans University
We prove the maximum principle and the comparison principle of $p$-harmonic functions via $p$-harmonic boundary of graphs. By applying the comparison principle, we also prove the solvability of the boundary value problem of $p$-harmonic functions via $p$-harmonic boundary of graphs.
Keywords: maximum principle, comparison principle, $p$-harmonic function, $p$-harmonic boundary, boundary value problem
MSC numbers: 31C20, 60J50, 94C15
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