Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics

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Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics 47
2014-03 発行

The dirichlet problem for ∞-harmonic functions on a network

Kurata, Hisayasu
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Description
We define the notion of ∞-harmonic functions on a network as a discrete version of that on a euclidean domain, and show some properties of such functions. We discuss the Dirichlet problems for discrete ∞-harmonic functions. We also show that limits of discrete p-harmonic functions as p → ∞ are in factdiscrete ∞-harmonic.