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Positive $p$-harmonic functions on graphs

이용하|김석우
대한수학회 (The Korean Mathematical Society)|2005.05|대한수학회보 (Bulletin of the KMS)|제42권 제2호|pp. 421-432

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참고문헌

주제분류수학

초록

Abstract

Suppose that an infinite graph G of bounded degree has finitenumber of ends, each of which is p-regular, where 1<p<infty.Then we can identify all the positive (bounded, respectively)$p$-harmonic functions on $G$.

참고문헌 (7)

  1. Th. Coulhon, "Vari'et'es riemanniennesisom'etriques 'a l'infini", 11, pp.687~726 (1995)
  2. "Rough isometries and p-harmonic functionswith finite Dirichlet integral", 10, pp.143~ (1994)
  3. I. Holopainen, "A strong Liouville theoremfor p-harmonic functions on graphs", 22, pp.205~226 (1997)
  4. "p-harmonic functions on graphs andmanifolds,", 94, pp.95~110 (1997)
  5. S.W. Kim, "Rough isometry, harmonic functionsand harmonic maps on a complete Riemannian manifold", 36, pp.73~95 (1999)
  6. Y.H. Lee, "Rough isometry and Dirichlet finite harmonicfunctions Riemannian manifolds", 99, pp.311~328 (1999)
  7. P.M. Soardi, "Rough isometries and energy finite harmonicfunctions on graphs", 119, pp.1239~ (1993)

관련 논문AI추천

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