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MAXIMUM PRINCIPLE AND COMPARISON PRINCIPLE OF p-HARMONIC FUNCTIONS VIA p-HARMONIC BOUNDARY OF GRAPHS
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 Title & Authors
MAXIMUM PRINCIPLE AND COMPARISON PRINCIPLE OF p-HARMONIC FUNCTIONS VIA p-HARMONIC BOUNDARY OF GRAPHS
Lee, Yong Hah;
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 Abstract
We prove the maximum principle and the comparison principle of -harmonic functions via -harmonic boundary of graphs. By applying the comparison principle, we also prove the solvability of the boundary value problem of -harmonic functions via -harmonic boundary of graphs.
 Keywords
maximum principle;comparison principle;p-harmonic function;p-harmonic boundary;boundary value problem;
 Language
English
 Cited by
 References
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J.-H. Kim and S.-Y. Chung, Comparison principles for the p-Laplacian on nonlinear networks, J. Difference Equ. Appl. 16 (2010), no. 10, 1151-1163. crossref(new window)

3.
M. Yamasaki, Ideal boundary limit of discrete Dirichlet functions, Hiroshima Math. J. 16 (1986), no. 2, 353-360.