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 Maximum principle and comparison principle of $p$-harmonic functions via $p$-harmonic boundary of graphs Bull. Korean Math. Soc. 2012 Vol. 49, No. 6, 1241-1250 https://doi.org/10.4134/BKMS.2012.49.6.1241Printed November 30, 2012 Yong Hah Lee Ewha Womans University Abstract : 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 Downloads: Full-text PDF