대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제42권2호
  • /
  • Pages.421-432
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  • 2005
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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POSITIVE p-HARMONIC FUNCTIONS ON GRAPHS

  • KIM, SEOK-WOO (DEPARTMENT OF MATHEMATICS EDUCATION, KONKUK UNIVERSITY) ;
  • LEE, YONG-HAH (DEPARTMENT OF MATHEMATICS EDUCATION, EWHA WOMANS UNIVERSITY)
  • 발행 : 2005.05.01
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⟨ 이전 논문 다음 논문 ⟩

초록

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

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참고문헌

  1. Th. Coulhon and L. Saloff-Coste, Varietes riemanniennes isometriques a l'infini, Rev. Mat. Iberoamericana 11 (1995), 687-726
  2. I. Holopainen, Rough isometries and p-harmonic functions with finite Dirichlet integral, Rev. Mat. Iberoamericana 10 (1994), 143-176
  3. I. Holopainen and P. M. Soardi, A strong Liouville theorem for p-harmonic functions on graphs, Anal. Acad. Sci. Fenn. Math. 22 (1997), 205-226
  4. I. Holopainen, p-harmonic functions on graphs and manifolds, Manuscripta Math. 94 (1997), 95-110 https://doi.org/10.1007/BF02677841
  5. M. Kanai, Rough isometries, and combinatorial approximations of geometries of non-compact riemannian manifolds, J. Math. Soc. Japan 37 (1985), 391-413 https://doi.org/10.2969/jmsj/03730391
  6. M. Kanai, Rough isometries and the parabolicity of riemannian manifolds, J. Math. Soc. Japan 38 (1986), 227-238 https://doi.org/10.2969/jmsj/03820227
  7. S. W. Kim and Y. H. Lee, Rough isometry, harmonic functions and harmonic maps on a complete Riemannian manifold, J. Korean Math. Soc. 36 (1999), 73-95
  8. Y. H. Lee, Rough isometry and Dirichlet finite harmonic functions Riemannian manifolds, Manuscripta Math. 99 (1999), 311-328 https://doi.org/10.1007/s002290050175
  9. P. M. Soardi, Rough isometries and energy finite harmonic functions on graphs, Proc. Amer. Math. Soc. 119 (1993), 1239-1248

피인용 문헌

  1. Positive solutions for discrete boundary value problems involving the p-Laplacian with potential terms vol.61, pp.1, 2011, https://doi.org/10.1016/j.camwa.2010.10.026
  2. THE -HARMONIC BOUNDARY AND -MASSIVE SUBSETS OF A GRAPH OF BOUNDED DEGREE vol.89, pp.01, 2014, https://doi.org/10.1017/S0004972713000439
  3. Graphs of bounded degree and thep-harmonic boundary vol.248, pp.2, 2010, https://doi.org/10.2140/pjm.2010.248.429
  4. The Dirichlet boundary value problems forp-Schrödinger operators on finite networks vol.17, pp.05, 2011, https://doi.org/10.1080/10236190903376204