Nagoya Mathematical Journal

Bounded energy-finite solutions of $\Delta u=Pu$ on a Riemannian manifold

Y. K. Kwon, L. Sario, and J. Schiff

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 42 (1971), 95-108.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118798303

Mathematical Reviews number (MathSciNet)
MR0287485

Zentralblatt MATH identifier
0193.07502

Subjects
Primary: 53.72
Secondary: 30.00

Citation

Kwon, Y. K.; Sario, L.; Schiff, J. Bounded energy-finite solutions of $\Delta u=Pu$ on a Riemannian manifold. Nagoya Math. J. 42 (1971), 95--108. https://projecteuclid.org/euclid.nmj/1118798303


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References

  • [1] J. Chang-L. Sario, RoyderCs algebra on Riemannian spaces, Math. Scand. 27 (1970).
  • [2] C. Constantinescu-A. Cornea, IdealeRnder RiemannscherFlchen, Springer, 1963, 244 pp.
  • [3] M. Glasner-R. Katz, Onthe behavior of solutions ofu Puat the Rqyden boundary, J. Analyse Math. 22 (1969), 343-354.
  • [4] E. Hewitt-K. Stromberg, Real andabstract analysis,Springer, 1965, 476 pp.
  • [5] Y.K. Kwon-L. Sario, A maximumprinciplefor bounded harmonicfunctions onRiemannian spaces, Canad. J. Math. 22 (1970), 847-854.
  • [6] Y.K. Kwon-L. Sario, Harmonicfunctions on a subregion of a Riemannianmanifold,J. Ind. Math. Soc. (to appear).
  • [7] Y.K. Kwon-L. Sario, The P-singular point of theP-compactification for u Pu, Bull. Amer. Math. Soc. (to appear).
  • [8] L. Myrberg, Uber dieIntegration derDifferentialgleichung u c(P)uaufoffenenRiemannschen Flchen, Math. Scand. 2 (1954), 142-152.
  • [9] Uber dieExistenz derGreenschen Funktion derGleichung u c(P)u auf Riemann- schen Flchen, Ann. Acad. Sci. Fenn. Ser. A.I. 170 (1954), 8 pp.
  • [10] M. Nakai, The space of non-negative solutions of the equation u pu on a Riemannsurface, Kdai Math. Sem. Rep. 12 (1960), 151-178.
  • [11] Thespace of Dirichlet-finite solutions of the equationu Pu on a Riemannsurface, Nagoya Math. J. 18 (1961), 111-131.
  • [12] M. Nakai-L. Sario, A new operator for elliptic equationsandthe P-compatification for u Pu, Math. Ann. 189 (1970), 242-256.
  • [13] M. Ozawa, A set of capacityzero and the equation u Pu, Kdai Math. Sem. Rep. 12 (I960), 76-81.
  • [14] H.L. Royden, Theequationu – Pu andthe classificationof openRiemannsurfaces,Ann. Acad. Sci. Fenn. Ser. A.I. 271 (1959), 27 pp.
  • [15] L. Sario-M. Nakai, Classification theory of Riemann surfaces, Springer, 1970, 446 pp. University of California, LosAngeles