Hiroshima Mathematical Journal

Dirichlet finite solutions of Poisson equations on an infinite network

Takashi Kayano and Maretsugu Yamasaki

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 12, Number 3 (1982), 569-579.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206133648

Digital Object Identifier
doi:10.32917/hmj/1206133648

Mathematical Reviews number (MathSciNet)
MR676559

Zentralblatt MATH identifier
0523.31005

Subjects
Primary: 31C12: Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14]
Secondary: 31C20: Discrete potential theory and numerical methods 39A12: Discrete version of topics in analysis

Citation

Kayano, Takashi; Yamasaki, Maretsugu. Dirichlet finite solutions of Poisson equations on an infinite network. Hiroshima Math. J. 12 (1982), no. 3, 569--579. doi:10.32917/hmj/1206133648. https://projecteuclid.org/euclid.hmj/1206133648


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References

  • [1] H. Flanders, Infinite networks: I -- Resistive networks, IEEE Trans. Circuit Theory CT-18 (1971), 326-331.
  • [2] M. Nakai and L. Sario, Existence of Dirichlet finite biharmonic functions, Ann. Acad. Sci. Fenn. A. I. 532 (1973), 1-33.
  • [3] M. Yamasaki, Extremum problems on an infinite network, Hiroshima Math. J. 5 (1975), 223-250.
  • [4] M. Yamasaki, Parabolic and hyperbolic infinite networks, ibid. 7 (1977), 135-146.
  • [5] M. Yamasaki, Discrete potentials on an infinite network, Mem. Fac. Sci. Shimane Univ. 13 (1979), 31-44.
  • [6] M. Yamasaki, Biharmonic Green function of an infinite network, ibid. 14 (1980), 55-62.
  • [7] M. Yamasaki, Quasiharmonic classification of infinite networks, Discrete Appl. Math. 2 (1980), 339-344.